A mother sent this comment:
“Here is a problem my third-grader brought home (I had to read it 3 times, and it took ME forever to work this–forget an 8 year old):
“Easton has been raising vegetables in his garden all summer. He plans to sell some of his vegetables at a local farmer’s market.
“He has selected 24 radishes, 30 onions, 16 heads of lettuce and 25 tomatoes to sell. He wants to display the radishes together, the onions together, the lettuce together, and the tomatoes together, and to place them in sets with equal rows for each kind of vegetable.
“He plans to put each kind of vegetable in at least 2 rows. Show ALL the different ways that he can display equal rows for each kind of the vegetables at the market. Write an equation for each way you find.”
Diane Ravitch's blog 
This is why so many children and youngsters hate math! They don’t really get the point! Do they? This is not education for the 21st century! This is an easy way to create a boring learning environment! EA
This math problem will indeed prepare the sons and daughters of the non-elite, who attend public schools, for the global economy because our sons and daughters will have futures as migrant workers for the rich plantation owners. Therefore displaying onions in neat little rows will be a much needed skill. The rich and powerful send their children to private school to be truly educated. They only experiment on and fail OUR children—never their own.
Yes, they will work for the Lords of the manor. What a bunch of hypocrites.
Here’s a parody of New York State Ed.
Commissioner’s pushing of excessive
high stakes testing and the dubious
and unproven Common Core
standards:
Jack, we’ve seen it.
And then, as soon as he sells any of the vegetables, the marketing display is ruined. What an ugly waste of math.
This is what needs to be exposed about the corporate argument. They are “raising standards” by dumping bushels of contorted nonsense on our children. This isn’t good math, or real math. What a remorselessly stupid exercise their whole “higher order thinking” hoax is!
Math is beautiful and rewarding for children. We’re Homo sapiens, because we invented it, and their little job as human children is to learn how joyful and natural mathematical reasoning is, and then take the glorious step into abstract operations with it when their mental organization has developed to that point. Piaget observed the transition repeatedly around age 12, but it can be delayed by ill-concieved crap like the CC$$ is handing out.
Certainly, our third graders should be lining toy vegetables up in their play stores, or at least circling the corn and artichokes in their colorful workbooks, so they can trade them three for two.
Easton’s farmer’s market is apparently a lot more fru-fru than mine, where they just put the different veggies in bins. LOL
This kind of [stuff] is a guaranteed hour-plus homework assignment on just this one problem. I have a kid who loves to arrange things on her own, on HER terms, who would be in tears by the end of this exercise. 😦
I LOVE math. But not THIS!
So does Easton cut one of the tomatoes in half to make two equal rows? Then won’t every vegetable need to be cut in half? When considering the equality of rows, should Easton allow for size in that 2-3 tomatoes may be as wide as one head of lettuce (that is if every vegetable is exactly the same size)? Does Easton have siblings named Bethlehem and Allentown?
Wow! LG, you are applying higher-order thinking skills which are so necessary on today’s ” global economy”. I would definitely give you high marks for your level of reasoning .. but alas.
This demonstrates just how limiting the CCSS are and the PARCC assessments that accompany them.
Absolutely Dead Boring! Meanwhile in a real school this third grader could be on multiple field trips to the local CSA’s that supply the neighborhood farmer’s market. She could learn the in’s and out’s of their green economy and then return to school where all the 8 year olds would cooperatively plan the garden they planned for the local park come spring. They would scour seed catalogues and online sites for best buys and compute both order and budget for soil nutrients, tools, water, raised beds and more. They would prepare a master schedule to cover weekend and summer maintenance involving all student families and then begin emailing close-by Master Gardeners to ask if any might volunteer a little time to stop in at school and review the plans in progress. Someone would telephone the FFA or the Grange or the Farm Extension folks (if they aren’t still on Shutdown or Sequester Budget mode) and request their assistance. But experiences like these might produce a crop of citizens that the Plutocrats can’t harvest for their low-brow, mean-spirited global agenda, so back to drawing circle in the workbooks.
Wow, love your math lessons, wish my 4th grade son had them.
That’s a really good, rigorous unit.
I have a master’s degree and have always scored well on standardized tests. This problem makes me feel dumb.
It seems more like a logic problem than a math problem. Like something for AIG kids who finish the math quickly and need something to keep them challenged. But we can’t make students into AIG kids just by giving them these types of problems, which is what I think some influential folks think right now.
AIG (Duane, it stands for Academically and Intellectually Gifted). Right end of the bell curve. Say IQ 125 and up. As far from average as average is from the left side of the curve.
Maybe if I give all my students harder songs to sing their voices will all become better! And they can sing 21st Century Songs, better, in the Global Economy!!
I’m OK with this activity IF it involved the actual radishes, onions, heads of lettuce, and tomatoes, was done in small groups, and didn’t require an equation at the end. It would be especially worthwhile if the kids understood the information Kathyirwin1 incorporated in her “real school”… but unfortunately this format would undercut the notion of rugged individualism that is implicit in solving this problem in isolation, would fail to offer “higher level thinking” activities, and would not prepare kids for bubble tests that will be used to determine the school’s and teacher’s sustainability.
I’m not sure this is a problem that lends itself to a “bubble test”. This is exactly the type of question that gets at whether or not a student has grasped multiplication in some semblance of a real-world setting. It’s not a very imaginative problem, I’ll admit, but I think it requires much deeper thinking than anything that I had in third grade.
Developmentally, I doubt that many 3rd graders are ready for this, however. It’s not that hard, but pretty abstract, unless you have manipulatives (like real vegetables) to help you. A caring parent will help the child model this situation in some way, but how many of our students have parents like that at home?
If it were a multiple guess test I hope that “none of the above” would be the correct answer.
What an abomination of a question for high school algebra much less for 3rd graders.
Kind of like the short answer question I encountered on a SAT 9 test*: Make as many math sentences as you can with the whole integers 0-9.
*This was in the mid to late 90’s, I was forced to help proctor it in a cafeteria full of test takers in the morning where the smells of lunch cooking were wafting through the air. Wonder how many others taking the test were distracted by that-standardized schmandardized. And, yes I read the whole test as I refuse to proctor a test without knowing what’s on it. There were “construction” problems with well over 35% of the questions. What a farce of a test.
Are you sure this isn’t a question from a psychology AP exam? Easton sounds a little OCD.
Glad to see that we are equipping our children with flat-world skills —schools never change. When I went to school it was figuring out when two trains would arrive in Kansas City–now we are arranging fruit and vegetables.
Flashback to train problems.Mine were with speed traveled, left at specific time, added variable was: throwing an orange out of the train window at a speed of 60 mi:hr as the train was traveling 75 mi:hr. In the opposite direction.
Q: what was served for lunch in the dining car of the TransContinentalRailroad?
Relevance…Schmelerance! Years ago there were some totally off-the-wall problems, NOW…test creators appear to compete with each other to come up with the most obscure crap.
A great use for these types of questions could be for a neighborhood pub on a Friday night for drunkards to solve. Could be fun!
Keep them away from our children.
“Relevance…Schmelerance!”
Hadn’t read your comment yet when I posted the above response. My thoughts exactly.
Not a fan of Common Core, but if this was the ONLY homework problem, it’s not that horrible and quite in line with what I having been doing with multiplication factors for many years (way before Common Core), with a few important qualifiers.
First: The problem is asking for factor pairs and the creation of arrays. Based on my copy of Common Core, that is more a Fourth Grade Standard, than Third Grade.
Fourth Grade: Operations and Algebraic Thinking: Gain familiarity with factors and multiples.
4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
I suppose at a stretch it could be considered.
Third Grade: Operations and Algebraic Thinking: Represent and solve problems involving multiplication and division. 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Second: The obvious, has the student been prepared for this with multiple examples in the classroom before this was sent home as homework? One of my personal favorites for presenting this type of situation in class is reading A Remainder of One by Elinor Pinczes and providing manipulatives for the students to create their arrays.
Third: Does the student have sufficient automaticity with basic multiplication facts to handle producing all the possible combinations without undue stress?
Fourth: Were scaffolding options suggested and available to the parent and student? manipulatives, multiplication charts, and EXAMPLE problems on the homework sheet.
Meanwhile the answers:
24 Radishes: 2 by 12, 3 by 8, 4 by 6, and technically – 12 by 2, 8 by 3, 6 by 4
30 onions – 2 by 15, (which is not a basic fact), 3 by 10, 5 by 6, and 15 by 2, 10 by 3, 6 by 5
16 lettuce – 2 by 8, 4 by 4, 8 by 2
25 tomatoes – 5 by 5
Thanks for your thoughtful comment, and especially for your citation of the actual common core standards.
I do not think the criticism is about the appropriateness of skills required to answer this question in 3rd grade–I think the criticism lies with the lack of clarity in this and the many other questions that come out of the reformist “rigor.” There are far too many “gotcha” questions that show up on standardized tests, especially those tied to teacher performance ratings, that may or may not be intended to confuse. When there is no intent, confusing students and then judging them by their lack of understanding of questions is unfair. When the confusion is intentional, the test-makers ought to be brought up on charges since they are not only affecting a child’s sense of self but they are harming the livelihood of the child’s teacher which in turn affects the teacher’s own family. Confusing, inadequate wording in testing and yes, even Common Core test preparation exercises should be very closely scrutinized–and let’s be frank about the fact that this question is most likely from the CC methodology.
“…to place them in sets with equal rows for each kind of vegetable.”
By the above statement, the student is to assume that each vegetable gets its own version of “equal rows” and not every vegetable must have the exact same number in its row. However, that fact may be misinterpreted. There are two qualifiers for the vegetable rows that might need more clarification: kind and quantity. To simply insert the word “kind” may not be enough. Some children may interpret equal rows of “kind” to mean that each row must be homogenous in terms of the kind of vegetable, but the quantity of each individual vegetable MUST be the same in every row (equal). For the students who think this way, there is no possible answer.
Now would a student come to the conclusion that he must interpret “kind” to mean that each type of vegetable can have its own version of quantity? Perhaps and perhaps not. He might just give up after he has learned that 30 and 25 cannot be divided up to have equal parts without a remainder.
The question ought to have the clarification statement to the effect that each vegetable may have a different number of items in its sets of rows from another vegetable and an example offered.
As a teacher of math, you obviously know what is implied, but some children may not, especially if they do not have knowledge of or experience with the objective, as you pointed out regarding a student’s background and preparation for the homework. All I’m asking for is more explanation in the question itself especially if one just like it ends up in the context of a standardized test with no objective stated as it would be in a teaching unit. Not everyone thinks like a math teacher.
“For the students who think this way, there is no possible answer.”
Student anxiously, excitedly waving his hand in the air: “me, me, me”
“Student anxiously, excitedly waving his hand in the air: ‘me, me, me’
Me, too. But then again, nobody asked us what we Spanish and music teachers thought about the question’s wording before including it in the new “rigor” of reform. I suppose we have to think like math teachers to follow the gist, and 3rd students also have to think like math teachers or they will get this question (and who knows how many others) incorrect. Then, they’ll be labeled with low scores and their teachers will be penalized as “ineffective.” Sounds perfectly logical to me!
I know this much: My colleagues are secretly unhappy with how little creativity these standards foster and how completely streamlined and black and white they are. My district powers must be onto it because the head of the math department is playing the part of the Borg Queen defending the CC math standards with a ravenous vengeance. Dissension is discouraged among the rank and file, and apparently “resistance is futile.”
Again, if the people writing these new standards and questions had a little more formal study in Philosophy and a little less in Psychology, they would know do a better job. IMHO.
This is a thoughtful and reasonable response. I concur.
If both those were 3rd/4th grade questions when I was in those grades (1963-5) I wouldn’t have had any clue whatsoever because I believe we were just learning simple multiplication in 3rd grade. (and the usual caveat of having scored above the 90th percentile on any math standardized test I took through high school)
Sev:
This very problem was cited earlier and produced an interesting discussion. I believe Corey pointed out that in 3rd grade they are using arrays and so, while I believe the wording of this problem is unnecessarily complex, at root there is nothing wrong with it given the context of understanding multiplication via arrays.
Like TE, I also appreciate your citing of the actual curriculum. It is very helpful.
Understanding multiplication via arrays is not developmentally appropriate. That is the problem with the curriculum. It is not the teacher; she didn’t write this problem. It was part of the curriculum material or CRA prep. The problem is not one random problem; it is indicative of an entire curriculum which is set out to be unnecessarily complex because it is not developmentally appropriate.
Blaming one teacher works better though.
Don’t dare hold those at the top accountable. When this does fall apart, and it will, guess who they will blame?
Those stupid, incompetent unionized teachers, that’s who!
I actually understand this problem and can answer it. It took me about 3 minutes to figure it out. The question is testing how well a student knows multiplication math skills and reading comprehension skills – the key wording of the question is putting the vegetables in at least 2 rows; place them in sets with equal rows. But it depends on how well multiplication has been taught in the class. The student here should memorize the multiplication table AND be given a visual demonstration of how multiplication works in real life (like the veges in this example). If this is not done, the student will not be able to answer the question.
This is the answer:
24 radishes:
2 rows of 12 (2 x 12)
3 rows of 8 (3 x 8)
4 rows of 6 (4 x 6)
6 rows of 4 (6 x 4)
8 rows of 3 (8 x 3)
12 rows of 2 (12 x 2)
30 onions
2 rows of 15 (2 x 15)
3 rows of 10 (3 x 10)
5 rows of 6 (5 x 6)
6 rows of 5 (6 x 5)
10 rows of 3 (10 x 3)
15 rows of 2 (15 x 2)
16 lettuce
2 rows of 8 (2 x 8)
4 rows of 4 (4 x 4)
8 rows of 2 (8 x 2)
25 tomatoes
5 rows of 5 (5 x 5)
Randi B. ~
Can I cheat off your paper?
US Standardizers honestly believe, it is a belief system, that one cannot live, prosper, attend and graduate college, have a successful career, pay taxes, raise kids, qualify for Medicare & die Rich (sort of) without knowing how to solve such obscure problems. One can actually achieve it and not be embarrassed or ashamed. Unlike, how our kids feel when we spend their youth with such nonsense.
I wish I could express my feelings better.
Maybe in my next life.
Working on it….:D
I understand the problem just fine as well. I also understand that the above work would take my math-gifted 3rd-grader with a perfectionist streak probably TWO HOURS to solve. And that is ONE PROBLEM. Wait a couple of years till the arrays have had more time to become internalized and second nature and you’re looking at more like 10 minutes even for that complex a problem. This is TOO BIG for third grade, not just for the complexity of it (and the lousy wording) but for the time and mental energy expected of children whose brains are, by and large, not REMOTELY developed in the way to work it out on paper, and working it out with manipulatives would also be time-consuming, come to that, although preferable to paper-and-pencil work.
Even if third-graders could do this math easily, does it follow that this is what they SHOULD be doing? Third grade is about 8YO, which is EARLY CHILDHOOD, people! These kids still need to MOVE, they need experiential play for learning, they need concrete as their primary mode of input/learning, they need to create, they need to NOT be doing hour after hour of pencil work, and did I mention they need to move? Why the rush to do this in Early Childhood? In Finland, this age child would only have had ONE YEAR of formal instruction that isn’t primarily play-based. Finland gets it. We DO NOT.
Thank you Deb. This is exactly how I feel.
I thoroughly agree with you; however, we will find the one third grader who can do it quickly and easily and use that third grader as the excuse to require that all third graders be able to do so.
Cynewulf:
There are no questions as convoluted and poorly worded as this one on the TCAP, as far as I can tell from looking at the tests and supporting materials. It appears to be a mistake by someone. We do not know who created this question.
Bernie, I’m sure you are correct. But, my comment was really a general observation of how education has been working over the last 20 years. Sadly, as the highest jumper sets the bar for everyone else, the vast amount of attention is then focused on the “bottom 25%,” while the higher jumpers are all but ignored. Despite all of the attention (and interventions), the low jumpers seldom make the required height on their jumps (at least not during that year). The jumpers that easily reach the required height don’t get the attention they need to push themselves beyond their current ability level.
As for poorly worded questions, I see them all the time on FCAT, FCAT prep materials, and the CCSS aligned textbooks that our county has acquired, not to mention the ones that appear in the news and on this blog from other states. Apparently, the easiest way to increase “rigor” is to design questions that are either trick questions or overly vague questions.
Individually, these questions, while problematic, are not an indictment of the CCSS (or the sunshine state standards before them in FL). En masse, though, they undermine the purported aims of these standards.
I started off thinking that the row size was fixed (as it would be in a store) and then thinking how who could fit the same number of vegetables in a row so
3 rows of 8 tomatos (1 left over)
2 rows of 8 lettuces
3 rows of 8 onions (6 left over)
3 rows of 8 raddishes
Then comes the problem that you can fit more tomatos in a row than lettuces because tomatos are smaller but they don’t give the relative sizes so I get stuck unless I make further assumptions e.g. 2 raddishes to a tomato.
And I was stuck on writing an equation for my answers because I was taught equations always contain an equals sign e.g. 5×5 is not an equation.
It really is a stupid question because kids can bring in prior knowledge about how stores displays goods and that can put them on the wrong track.
It would have been better to ask for the knowledge directly instead of writing a convoluted question that doesn’t match the real world.
I think that as a strategy to get students to hate math, this assignment is brilliant and truly inspired!
I disagree. I think the issue here is that students have to learn how math is applied in the real world BEFORE such a question is asked. Math becomes much easier when students are given visual, real world examples.
I think students need to know how to multiply to be able to answer this “question” (sic). How many third graders are able to “go backwards” from the total amount to all the factors involved?
This is not how math is applied in the real world, and such a question is pointless and stupid.
Starting from stupid, it goes downhill. How are the pointlessly factored and arrayed vegetables supposed to be expressed in an equation?
And be careful if you ask them to do it with real onions, because they’ll discover the hexagonal close-packed array.
How many urban (and even rural) poverty district’s third graders even know what the items are????
This sounds like what’s called a math “task” on a constructive response assessment, which is supposedly in line with the way cc will be assessed. One task will assess many skills, as mentioned in previous comments. So much of the validity of this as a homework assignment depends upon what the child has already been taught.
Having seen a lot of math CRA tasks across grade-levels, this one is comparatively straight-forward. The whole point of these assessments, we’ve been told, is to get kids thinking about and applying their math skills in different ways. On the surface, this sounds great! But we are finding that so many of those claims about the cc standards, not just math, aren’t turning out as they were presented. Rather than freeing teachers and students to focus on creativity and problem-solving, they (perhaps I should say the assessments, rather than the actual standards) do the opposite. Assessments are designed in vague, confusing, often misleading ways. At first glance, perhaps when a textbook committee is evaluating their choices of core-aligned texts to adopt, the materials and assessments do appear to challenge students to think deeply and critically. But then, guess what! There is only one ” right” answer! There is only one “right” way of solving the problem.
I have found this whole mess to be damaging and stifling to children of all ability levels. My lower-functioning students are completely frustrated and soon give up (ironically, one initial claim was that students with disabilities would probably be more successful at this type of math task, since they are often visual learners). Some higher-functioning students tend to over-analyze this type of problem, and since it doesn’t take them long to figure out that there will only be one correct answer, they freeze.
Amen!!! This is what our local teachers are finding as well. I am so frustrated and heart-broken for them. Sadly, our best and brightest are leaving the profession. The stress and unfairness of CC is not worth it.
So sad because their intention was to weed out the “worst and the dumbest”.
Who will be left?
A revolving door of the pompous “Teach for-a-whilers”?
This would be a great classroom problem, maybe for a small group activity, with manipulatives. I can see how solving problems like this could prepare a third-grader to develop a deeper understanding of multiplication.
Developmentally, third-graders are still needing concrete learning. When you introduce higher-order thinking before they are ready, it handicaps their learning in the long term.
I can see how solving problems like this could prepare a FIFTH-GRADER (or older!) to develop a deeper understanding of multiplication.
I can also see how problems like this are destroying my younger child’s confidence with math, even though math/numbers/spatial stuff is one of her strengths. To me, that is BY FAR the bigger issue!
I think there are many ways to make mathematics unappealing to students.
And this is one of them and the original point of the post.
For some students you are no doubt correct.
I think it would be best not to do what the Tea Partiers are doing with respect to the common core. They’re posting all over the internet examples of individual lesson materials they object to for one reason or another and then implying or outright stating that this is what the CCSS is, as if the CCSS dictates this problem about radishes and onions–it doesn’t.
There is much to criticize in the CCSS on its actual merit–no need to resort to these straw-man arguments.
Dave, the assessments and packaged lessons are what the CC$$ is about. Look at the Pearson boondoggle in LA. Working backwards from the assessment boundary inevitably results in shallow curriculum , and garbled understanding.
The examples of standards-based chemistry on your website are very weak, for instance. The application of the second law in chemistry isn’t way different from pontificating that you can’t create perpetual motion machines, and the alignment of groups on the periodic table is more than a historical artifact. Yes, you can benchmark the standards to answer test items, while achieving no understanding whatsoever of the actual content.
If the Gates/Pearson axis makes your standards sufficiently convoluted and bizarre, and hides them behind an elaborate new “assessment vocabulary”, kids can be made to cry and fail as they gain no understanding, even when they do purchase your crap.
This isn’t a straw-man argument. This was my child’s homework problem. And it is an example of what he was required to do on a CRA (practice for the PARCC) test he took on Wed. It is NOT developmentally appropriate, so it does nothing but frustrate the students. Additionally, the questions are purposefully worded to confuse the students. And this is consistent on daily worksheets, weekly tests, etc. that we see from the textbook companies. But we can’t create an educational crisis if we actually look at the student as a whole, and look at whether or not they are functioning at a developmentally appropriate level in educational matters. We can’t fork over millions of dollars to these companies (Pearson) to help us “teach/save” our children. Finally, I feel for the teachers. Their jobs are on the line because their evaluations are tied to these tests with purposefully confusing questions, tests designed for children to fail.
In third grade, children desperately need concrete experience in multiplication. This past week, I had to teach 15-year-olds how to figure out the formula for aluminum oxide (Al2O3), based on the aluminum cation having a +3 charge, and the oxide having -2.
They need to visualize that 2×3 = 3×2, without performing the physical operation. They can’t, so I show them Piaget’s block game with 5-year-old Pat. They’re fascinated by that. There’s nothing wrong with them, except that ten years ago, poverty and corporate education reform took away their blocks.
I share the following as a way to make the case for taking the learning process into the real world of a garden as a means to investigate math and many other concepts back in the classroom. It’s a 5 minute video that illustrates the power of a school garden.
Thanks, David. It made me cry with joy.
We did this in California, at my youngest son’s primary school. We made a gourd and bean teepee, a corn spiral, and a sunflower house, as well as the rows. We took turns watering over the summer, and had the produce for our harvest festival. Twenty years ago, I now realize!
Everybody, go do this for today’s children.
To me, just typical of the standardized crap put out by standardization freaks.
I’m a little baffled by the reaction to this. What’s wrong with the question? (And please do not tell me “this is not how math is applied in the real world,” as if everyone’s “real world” is the same.) It does seem hard to me for third grade, but it’s simply a homework question for them to try and work out; whether it is appropriate or not would depend on a multitude of other factors we don’t have here.
I’m a high school English teacher, and I can’t help but draw an analogy to the blitzkrieg of “what does this have to do with my life?” complaints we sometimes get when we assign a challenging piece of literature to read and study.
The question is not developmentally appropriate. Students at this age (there are exceptions), need concrete math. If they do not get a good foundation in the concrete, they will be unable to do the abstract when they ARE developmentally ready for it. LIke you, I teach English (community college). I would rather my students come to me with a mastery of the concrete (grammar, complete sentences, paragraph structure, etc). Then, I can teach them how to form an argument and support it logically ,etc. Instead I find myself having to teach basic grammar because my students cannot begin to write and support a logical argument when they cannot even write a complete sentence. Because we are teaching higher-order thinking skills too young, our students are not getting a foundation on which to build. Kindergarteners are learning about persuasive writing instead of what is age-appropriate.
The above questions are purposefully designed for the children to fail. That is what CC is all about. They are setting our students up for failure so that the backers can privatize education and make a fortune in the process. I have 4 kids in public school, and I have seen a drastic difference in their school experiences. It breaks my heart for the younger ones. Honestly, unless there is a huge reversal on CC, I may have to homeschool, not something I really want to do.
You hit the nail on the head.
It is absolutely frightening when I think about years of such damage to our kids and their fractured education.
Gates and his SuperRich CCSS buddies need to keep their money-grubbing hands off our kids! Will there be a Nürnberg Trial for education some day? Damage to zillions of children in US?
We have no choice to speak up. Cannot be silent, ever!
H.A.
In my opinion, you are vastly over-reacting. I agree that the question is poorly framed, however, the previous discussion string on this same topic suggests that the homework assignment was created by the child’s classroom teacher, presumably after lessons in arrays and multiplication. The end of the world is not nigh and allusions to Nazis is inappropriate.
Sorry, Bernie, but the context if the question is key. Regardless of whether or not it was homework, it was preparation for a standardized test, and a poorly written question at that.
Here is the explanation from Melody:
“This isn’t a straw-man argument. This was my child’s homework problem. And it is an example of what he was required to do on a CRA (practice for the PARCC) test he took on Wed.”
bernie1815 ~
No doubt, I may be overreacting. However, these types of questions are not an isolated incident. We can nitpick each question and sort out parts that are and are not appropriate for the specific grade. Overall, our young children are given content that is not appropriate! We act as if there is NOTHING AGE APPROPRIATE TO LEARN. Who invented that nonsense? Just because a 4 year old can parrot “Tolstoy” does not mean we should teach it. God, I hope we can agree on that. Unless, we are in Russia. May have a point. NOT!
Years of out-of-reach instruction is harmful and wasted! Not another opportunity to fix it, for most.
Sorry, did not mean to offend anyone about Nürenberg. Understand!
H.A.
I do not know whether such poorly designed questions are typical in CC workbooks or not. I do know that more than one badly worded question from an unknown source is needed before making sweeping generalizations.
Again, I fully agree that this is a poorly designed question. It is too complex and has an ambiguous, for me, term, namely “equation”. On the other hand, we do not know the context and the nature of the lesson preceding the homework assignment. Imagine if you were the teacher who gave this assignment and had to read these comments.
Jim, I appreciate your willingness to ask why the strong reaction. That’s a perfectly legitimate question and it’s one reason I love this blog so. We are all learning from one another. I’ve certainly been made aware of many issues I wouldn’t have known about otherwise, simply because they aren’t part of my daily experience. I also appreciate that you brought up the “what does this have to do with my life” complaints. We teachers and parents all know a good education does include learning and doing some things that a child can’t directly see a future need for. I do sometimes worry the general public may be led to believe that complaints about cc aren’t valid because they’re just coming from people who don’t want the “increased rigor”. We have to counteract that by exposing the truth of the situation.
I can’t speak for anyone else here but I’d like to share the reason this is troubling to me personally.
If I had to guess, the teacher gave this assignment to help his or her students prepare for a CRA, and rightly so since these are precisely the types of problems encountered on the CRAs. This would be one of 3 or 4 tasks on the CRA.
Given LOTS of time to explore, use manipulatives, etc, parts of the task would be fine for helping children understand the whole concept of multiplication. Sad thing is, the teacher most likely feels an intense pressure to quickly cover lots of skills and content. I truly doubt the teacher will be able to devote the time to teaching these concepts in the way he or she believes best.
Depending on this teacher’s administration, he/she may even have to follow a scripted program or a rigid curriculum that would do away with any opportunity to turn this into a hands-on learning activity anyway. Sad, but factual….I witness this daily and have friends in other school systems who are dealing with these issues.
You are exactly right. In Florida, this was happening even before CCSS and has only gotten worse. Students are leaving elementary school without a solid foundation of basic skills. I’m not even talking about the students who are “below grade level.” But they’ve all gotten a drive-by’s worth of exposure and practice with various higher order skills…
LG’s got the best take on this, and his analysis is exactly why I was initiatlly stumped by this problem:
““…to place them in sets with equal rows for each kind of vegetable.”
By the above statement, the student is to assume that each vegetable gets its own version of “equal rows” and not every vegetable must have the exact same number in its row. However, that fact may be misinterpreted. There are two qualifiers for the vegetable rows that might need more clarification: kind and quantity. To simply insert the word “kind” may not be enough. Some children may interpret equal rows of “kind” to mean that each row must be homogenous in terms of the kind of vegetable, but the quantity of each individual vegetable MUST be the same in every row (equal). For the students who think this way, there is no possible answer.
Now would a student come to the conclusion that he must interpret “kind” to mean that each type of vegetable can have its own version of quantity? Perhaps and perhaps not. He might just give up after he has learned that 30 and 25 cannot be divided up to have equal parts without a remainder.”
And what of the directive for the algebraic formula? It this appropriate for 3rd grade?
ME:
You made the same mistake I did in reading the problem. It does not ask for an “algebraic formula”, it asks for an “equation”, e.g., 24 = 2 x 12. It is that simple and developmentally appropriate. I do agree the problem, created apparently by the child’s teacher, is poorly worded.
How do we know it was apparently created by the teacher? My guess is no because it was part of test prep. Now why would this question be so totally different from one that will be on the test?
LG:
Because I asked the mother for a reference to the book it came from and she said it was on a worksheet with no identification. It is a reasonable inference on my part.
To be clear, I agree that the wording of the question is bad. If it was from a math workbook, it is worse.
Please check the earlier string.
EGADS…there are all kinds of things wrong with the question. First, it’s developmentally inappropriate and worse yet, what does this question VALUE? Answer: the Corporate agenda. Look at this question again and unpack what it values.
Yvonne:
Such a mighty edifice constructed on a poorly worded question of unknown pedigree and without a morsel of evidence as to its context.
This problem has the potential to align to the following CCSS standards:
3.OA.A3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
4.OA.B.4: 4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Which one it aligns to would depend on whether the teacher is asking the student to (1) write one equation for each vegetable (5 x 5 = 25), (2) write all factor pairs, or (3) one equation for all vegetables (6 x 4) + (5 x 6) + (4 x 4) + (5 x 5) = 95.
The problem with the question lies in it’s vagueness around what it is asking for, but the problem itself is not developmentally inappropriate for a 3rd grade student. I taught 3rd grade, and we worked with arrays – rearranging them and writing equations for them. They loved it! (Granted – we used Smarties… 😉 The reason this parent may have had trouble is because when we were kids we most likely did not use smarties or vegetables to help us understand multiplication – we memorized math facts from rote with little understanding of why or how it worked. This is one of the major reasons for students’ struggles with higher math – they try to memorize the formulas without understanding why or how they work.
Anything in ANY set of standards, including the CCSS, can be developmentally inappropriate. It depends on its application. This is where teacher professionalism and autonomy is paramount – teachers need to be able to take a problem and ensure that it aligns both to whatever standard they are aligning it to AND is developmentally appropriate for their students.
Never had the CC, and I know I memorized multiplication facts in third grade. As an adult, I use math everyday. Never complained how it was going to apply to me at any point while I was in school.
Absolutely, situating learning in life is an excellent teaching strategy. Thing is, not every student can nor needs to know every single purpose for learning every single something. The explanations would take far too much class time, and many can be far beyond a student’s developmental ken.
CC is just another re-invention of the wheel. Is it an improvement? We shall see, but I do not feel like the math study I had in Pennsylvania’s public schools was inferior. Nor was my brother’s– one of the people who developed the broadcasting constant for high-definition television.
Perhaps he would have done something “far greater” had he been taught via the CC math standards? 😉
CinD:
Thanks for the additional background and context. Do you think that the change in terminology, e.g., arrays, leads to confusion among parents and a miscomprehension of what is actually going in the child’s class. I still recall the times tables on the back of every school notebook. However, I can see the value of arrays. In fact they make more sense to me than number lines do.
Lest I be pilloried I hasten to add:
To assuage some here I apparently have to declare that I am not a K-12 educator, merely the father of 3 kids and husband of a former HS teacher.
I agree with you that teacher professionalism and autonomy are paramount. That is precisely what we are losing. I’m know there are plenty of schools out there where teachers still feel that sense of professionalism, but that’s quickly changing as the pressure continues to build.
For those who don’t see a problem with this math task or with the standards in general…you may not be aware of what’s happening in some cases. One of my biggest concerns is the core-aligned curriculum districts feel pressured to adopt. Pearson is making a killing off feeding our fear; they are offering up their materials and programs as the way to help students do well on high-stakes tests. Makes sense, since they also make the tests. When students don’t do well on tests and intervention is required, well…any guesses as to what company swoops in with their intervention kits and computer programs, ready to save the day?
This parent had a problem with it because it only further complicates something that should be concrete at this age. I get that there is a deeper understanding of math that many enjoy. But it is not for everyone and it further complicates an issue that could be within the grasp of a third-grader. I am fine with moving on to the more abstract with older kids, but I am not fine with it here. I am watching my son’s confidence crumble with the CC math. And the thing is, I don’t blame him. He shouldn’t be able to do all that they are asking of him.
And for the record, I did merely memorize my multiplication facts: in third grade. And I am thankful that I did so. It gave me a foundation to use in the future in school and beyond. In fact, I use them on a daily basis. I am glad that I don’t have to stop and draw pictures and equations and work backwards to figure out an estimate of what my groceries are going to cost. You may find the beauty in the depth of math. I find it in a piece of literature. Even though I love to analyze and look for the layers of meaning in a work, I fully understand that most people don’t. Most people just want to read a story to enjoy it, and I am ok with it. Most people just want to be able to use math, and I think we need to be ok with that as well.
That said, I am all for exposing students to the more in-depth concepts of any subject – when they are developmentally ready. If we continue to force too much too young, their brains are not truly understanding the higher-order. I guess my main point is that we have to learn the concrete before we learn the abstract. Learning the abstract without the foundation of the concrete is disastrous.
As a written question, very few 3rd graders would get it. If you gave them a set of 12 objects and asked them to experiment and see how many combinations of rows they could make, most of them would do just fine. So, I think the concept is fine, it is just the presentation that leaves a little to be desired.
Nothing wrong with repitition, but why not lay out the example first, instead of the details for four examples and then the instructions? What’s up with that?
WTF Seriously??
As to the reformers chuckle-headed machinations, you’ve summed it up perfectly.
TC:
The evidence available suggests that this question was created by a teacher after a class that presumably looked at arrays. It may or may not reflect broader educational issues but unhesitatingly linking a poorly worded math question to the possible machinations of rich, misopedic, corrupt, profit-seeking reformers defies both logic and gravity.
Says one non educator, named Bernie.
There’s lots of prepackaged common operating system crap peddled by the edufrauds.
B E W A R E and BE AWARE.
Linda:
What is a “prepackaged common operating system”?
Oh Bernie, you know….the national standards bring foisted on the little people by bumbling, bloviating, billionaire buffoons. Silly you.
New word for me: misopedic. I’ll add it to misanthropic, mysogenistic, et al.
Bernie, please see my comments above. They may help you understand why so many find this problem so upsetting. If I didn’t have the opportunity to see the bigger picture on a daily basis, I might also question the strong reaction. But there really is a lot more going on than most people realize.
Bookworm 23:
I am no fan of text book publishers. My wife teaches ESL. The costs of what are essentially brightly colored compilations of National Geographic and Smithsonian articles are outrageous. That said, the issue of how much money Pearson makes is only relevant if it means that schools are spending significantly more now than in the past. If you want to ensure competitive pricing push for a fair use doctrine that allows for more extensive copying of curriculum related materials that are protected by copyright. If Pearson want the test revenue, they should be required to give up their copyright on their textbooks.
That said, I still see no reason why the curriculum per se should limit the creativity and ingenuity of classroom teachers. Take the TCAP test that the original post raised.
Click to access ACH_2012_PracticeTest_Gr3_Feb13.pdf
I would like to hear from a 3rd Grade Math teacher who believes that they could not address the math materials covered in these tests with their own worksheets, exercises, materials, hands on experiences and board work. All these practice test materials and item samples are freely available.
Bernie1815
Just because there is no identifying info on it, does not mean it was teacher-created. Believe me when I say that teachers no longer have the autonomy or time to create their own worksheets. They frequently use databases, etc. It is more likely she used cut and paste, and put the one problem on the worksheet. But honestly, whatever the problem is, it is merely a scratch on the surface of the idiocy and restriction of CC.
Melody:
It seems to me that we still need to hear from the teacher as to where the question came from and what he or she thinks about it.
I found item samplers and sample tests for the TCAP here:
http://www.tn.gov/education/assessment/ach_samplers.shtml
Do I have the right tests?
I went quickly through these Pearson published tests and the sample items. The Math questions are all simple and straightforward and there was little that I thought an 8 year old would not be able to answer. (Trapezoid was an option in one question which I thought was a silly and unnecessary option.) They include a number of questions about simple pictorial models to convey basic ideas – which are essentially equivalent to the notion of arrays, but I could not find a question that specifically dealt with arrays.
I did think the tests were too long – 55 math questions for this test
Click to access ACH_2012_PracticeTest_Gr3_Feb13.pdf
A number of the questions did seem redundant.
Melody:
My response got stuck in moderation because of links.
Melody:
It seems to me that we still need to hear from the teacher as to where the question came from and what he or she thinks about it.
I found item samplers and sample tests for the TCAP here:
http://www.tn.gov/education/assessment/ach_samplers.shtml
Do I have the right tests?
I went quickly through these Pearson published tests and the sample items. The Math questions are all simple and straightforward and there was little that I thought an 8 year old would not be able to answer. (Trapezoid was an option in one question which I thought was a silly and unnecessary option.) They include a number of questions about simple pictorial models to convey basic ideas – which are essentially equivalent to the notion of arrays, but I could not find a question that specifically dealt with arrays.
No, the TCAP is somewhat straightforward math. We will no longer be doing the TCAP after this year. These type of problems are what the students are doing now in preparation for the CRA (which our practice test for the future PARCC tests, which is testing the new CC math). The CRA was only 4 questions (they took it this past Wed), and they had to spend 15 minutes working each problem using the CC method of doing math. One problem had to do with finding area. I don’t understand the CC way, but apparently it takes the full 15 minutes to work it out, draw pictures to explain it, and then write complete sentences about the why of it all. If they work it the CC way and get the wrong answer, they at least earn 1 point (I think they are graded on a 4 pt. scale). But if they work it the traditional way and get the correct answer, it is worth 0 (I think they are graded on a scale of 4).
I just do NOT care if my child can write 3 sentences explaining WHY he found the answer the way he did. I do NOT care if my child can draw a nice picture which further explains his answer. I care if he got the correct answer. If he has a basic understanding of how area works. The other stuff is a WASTE of time.
Melody
Part 2
I did think the tests were too long – 55 math questions for this test
Click to access ACH_2012_PracticeTest_Gr3_Feb13.pdf
A number of the questions did seem redundant.
To keep “improving” schools perhaps some day we will be teaching kindergartners quantum mechanics and calculus.
Well, we wouldn’t want to impose the soft bigotry of low expectations on our kids…
We have a cohort of math teachers at varies grade levels developing unit tests and practice items. I don’t thing they have time to take a second look at their creations or get an outsider’s opinion.
This is what happens when change is implemented in a school district; it is always done haphazardly. They pick their guinea pigs to be on math committees which some of them feel important. Then they are required to slap together a unit test in a couple of months. This math question could have been a result how it was created.
Having teachers develop tests are fine as long as they understand how to create questions. One has to be cautious of biases and perspective that can affect the testtaker. The questions must be clear to the reader so the it can be answered the way it was intended–reliability. The question must also be valid. If it is made up and thrown in just to meet a standard, then what’s the purpose other than torturing the testtaker?
And torturing the teacher…
Torturing the “Former Teacher” that is now the “Present Tester”
Here is your lesson for today…
I want you to build an airplane..in the air..
Now go along….discover what you need to do then do it…..
I am here if you need me….and remember the test will be this Friday on what you have learned..
Due Friday
1. 7 page essay on your discoveries while you were in the air
2. 20 math problems…you have to guess what the questions might
be..but beware..you have to figure it out on your own.
3. The history of airplanes
4.What makes an airplane fly essay-single spaced..10 font..Times
New Roman…at least 4 pages..
6. and blah and more blah and more blah and more blah and more..
Students..there is not time for physical activities this week
Do not listen to any music..Do not watch tv…
You will not have time…and it distracts you
You need only to focus on the Test(s)!!!!!!!!
I know it is fair week but you must not go and if I see you there I will subtract 20 points from your final grade…
I expect you to tweet me how many hours you are spending on these assignments.@Tester Teacher every hour on the hour..
This date will be given to the main data folks that are (into blossoms)
Try to get at least 4 hours sleep each night and get your Mama to take you by the fast food that has the dollar menu for breakfast.
We do not have time to stop working..
We do not have time to listen to music..
We do not have time to play…
We only have time to teach you what is important..
****************
Just remember how you built that lego tower starting at the top and do the same for the airplane…
You are not allowed to have a foundation….You can figure this out.,.I know you can..
**********************************
And…for the Rocky Top word problem
I will give you the number
You will figure out as the famous Greek Mathematicians did ..how to factor these numbers..
Get your mother and/or father to buy each vegetable…..
Once you finish this question you should see that 1 x 24 = 24 and so forth..
Naw..don;t use one….start with 2
OK..2 x 12 = 24…..
Vocabulary
Array….Martrix…Matrices….Factor…Factoring…Multiply
Oh..make sure you know how to count from 1 to 24..
Have a good week…and good luck..
I am your facilitator and proud of it..
I can not help you get into the air…ask Bill and Mr or Mrs Pearson..
or,..maybe Arnie…
This problem wasn’t created by teachers. It can be found on the Tennessee Common Core site and is likely a problem being used around the country.
If this was a practice test question, then it is more than likely it was developed by teachers. If it was a state test question, it was developed by people at state level. Once CCSS assessments are put into place, all students will be taking the same test.
But whatever tests kids are taking these days, there are always going to be questions like the above. The takeaway is that it is ridiculous to give kids high stakes tests period and to use instructional time to practice for them. Testing doesn’t leave much options for kids’ future. Graduating from high school shouldn’t be a 50/50 chance which means reformers are gambling with kids’ lives.
Many comments have been made about the age appropriateness of concepts, but surely there are a range of abilities in students that is independent of age. This is explicitly recognized in high schools where students of the same age may be taking very very different mathematics classes if they are given the opportunity.
I have two questions that I hope some posters here might be able to answer.
First, what percentage of students of a given age must be able to answer a mathematical question or use a mathematical concept for it to be considered age appropriate?
Second, at what age do public schools stop working about age appropriateness and start thinking about classes that are ability appropriate?
High school is a different ballgame than elementary school. I taught high school, and I currently teach at a community college.
To answer your first question: It isn’t so much about judging what math problems, etc. they can do. It is more about biological development. Psychologically, MOST children of a certain age are biologically equipped to do certain thinking tasks. In early childhood development, that ability is limited by the fact that most children can do concrete tasks, but can’t do abstract. Yes, there are exceptions (and those are usually in gifted programs), and yes, we should challenge kids, but when you push them to do tasks that they aren’t developmentally ready to do, then they shut down and feel like failures.
Second: Middle school is usually when they start to ability group, at least where I am.
By most, do you mean 51% or a supermajority?
How tight is the link between biological development, academic performance, age, and environment? It seems to me that the majority of folks who post here would argue that a question which might be appropriate for children raised in a high income household with concerned and caring parents would be inappropriate for a students raised in poverty with uncaring adults in his or her life even if they are in the same grade and the same age. I should add that there can be over a years difference in age for students in the same grade in my local school district. Does that change what is appropriate for a grade?
It is middle school in my district as well, but without any gifted program the only solution for those students is to skip a grade in the regular system.
I think developmentally appropriate is a supermajority. If you read a lot of the early childhood psychologists comments on the early ed portion of CC, they take issue with it. When elementary school teachers go to college, they have to take psychology classes to learn what is biologically/developmentally possible for the majority of kids.
So when I say developmentally appropriate, I mean for all kids, no matter income-level. We are a pretty solid, middle-class family, and I find this inappropriate for my child, as do most parents I have talked to. And from what I am finding online, it is mainly middle-class, solid families who are taking issue with the developmental appropriateness of the math. Which means, it is probably that much worse for poverty-stricken kids who may or may not have parents who have a clue as to what is going on.
I was talking to a middle-class parent the other day who was frustrated because her child was struggling with a particular skill in the first grade. She thought her child was just “dumb” for lack of a better word. She had no clue that her daughter should be struggling with the skill not because she was dumb but because biologically she wasn’t ready to do the higher-order thinking skill.
You are right that there are age variants in any grade, but I believe that there is a target as to what is developmentally appropriate and still pushes kids. And I also believe that teachers are able to do this at different levels, without the ridiculous tests, etc.
If anyone is interested, here are the teaching notes for this problem
Click to access Grade%203,%20selling%20vegetables.pdf
Courtesy of google.
Thank you for posting the source! I suspected this was a CRA task.
Oh, shoot! Now we can’t blame it on one teacher. Damn!
Linda:
TE found the source. I had asked for the source from Melody earlier this week. Now I have additional facts and it appears that the question is on a published source. It is a phenomenally bad question and completely wrong. The question is so bad, I find it hard to believe that any responsible person would put this question together. It is bad, what more can I say.
TE
Great find. Can you share your search term? I went looking and mistakenly end up in TCAP. This question format is totally bizarre. It amounts to a requirement for almost 100% proficiency before being able to solve the problem. Lousy item design.
I just copy pasted the entire question.
TE:
Shoot, I tried bits and pieces. Good job. What is your take on the question now that we know that it was a single complex question.
So, Bernie, teachers and parents keep trying to sound a much-needed alarm. Whatever they might say, you look for a way to denigrate them. Yesterday, for instance, you constructed this fantasy scenario:
“The evidence available suggests that this question was created by a teacher after a class that presumably looked at arrays. It may or may not reflect broader educational issues but unhesitatingly linking a poorly worded math question to the possible machinations of rich, misopedic, corrupt, profit-seeking reformers defies both logic and gravity.”
The source teachingeconomist found directly shows the power and reach of the CCSS monstrosity. It’s a market-domination scheme. It holds little children “accountable” to it, and forces compliance through actual statutes enacted in stealth and corruption. It does reflect the “machinations of rich, misopedic, corrupt, profit-seeking reformers.”
You say you’re the father of three, not an educator, and your wife is either a former of current teacher. Nobody is “unhesitatingly” linking anything, and in fact we’ve hesitated far too much. What motivates you to defend the CC$$ profit drive so tenaciously?
Yes, chemtchr…..so well said. I would love to know.
He’s very vague when asked about his profession. Maybe he’s in on the reformy gravy train.
It seems to me that 3-5 people comment here who are possibly stirring the pot and trying to divert the conversation. So I wonder if they are trolling for the reformers!
chemtchr:
Nonsense.
As soon as Melody raised this question I asked for the source. I already noted that the question was poorly worded and too difficult for a 3rd Grader. She was unable to find a source. I looked but came up with the wrong source. Then TE found the source and the terrible question was worded and framed exactly as Melody presented it. So after the evidence was provided the incompetence is down to the Pearson test item designers.
I am not defending CC. I am not defending Pearson. I am arguing that people should have evidence before jumping up and down. When they have the evidence they are entitled to jump up and down.
The problem here is we, the teachers, see evidence every day and you do not. I personally don’t feel the need to prove it to you. Sooner or later you might catch on.
Linda:
I am retired. I have no connections to the Ed Reformers or any publishers. You have asked the same question before and I said the same thing.
When issues arise I politely ask for evidence. Only Teaching Economist presented it. I said from the start that the question was very poorly written. So poorly written, that it is hard to believe a test writer would do it. But someone did.
You’ve never identified your profession or your area of expertise. This single question is only the tip of the iceberg. It is much worse. This will all collapse eventually. Who will you blame?
Bernie, I’m sorry other people suggested motives for you here, because my question is a serious one. Many who aren’t directly “on the gravy train” have a similar pattern of thinking, and I ask you, “What motivates you to defend the CC$$ profit drive so tenaciously?”
You answer, “nonsense”, but then you don’t turn your analysis to the question of why and how such a question was inflicted on an eight year old. If you’re motivated by intellectual curiosity and interest in educational questions, what (still) stops you from going in that direction?
chemtchr:
I am not defending anyone. I am arguing for data and evidence before making judgments, attributions and evaluations.
I see no problem with any publisher making a profit. I do see a problem when there is some kind of monopoly and I suggested a way to break the linkages between test publishers and textbook publishers, namely, making the textbook publishers give royalty free licenses for their textbook materials where they have a test contract.
As to how such a question got framed, I will try to find out though others here could do this also now that we know where it comes from.
As I noted this type of question is bad on many grounds from a psychometric and efficient test design point of view. It would be a badly designed question for 13 year olds and it is a terrible question for 8 year olds. It seems they want to determine whether the kids can sift through multiple issues. This in itself is not a bad strategy for much older kids – assuming that they expect multifaceted questions and the question itself is clearly worded.
A good example of integrating multiple concepts is on the 6th-grade Singapore Primary School Leaving Exam. It can be found on Page 38, here.
Click to access hjk_working_paper_12.10.12_0.pdf
It presents two rectangular tanks of different dimensions. One tank is filled to the top with water, the second tank is empty. The students are asked to calculate the height of the water when both tanks are filled to the same height using the water from the filled tank.
Most tests are designed to include easy, moderately difficult and hard questions. Using the above water tank example, a harder question may include spheres or semi-spheres as the containers on the assumption that the calculation of the volume of spheres is more difficult.
If the vegetable question was trying to emulate this approach it simply failed, in my opinion. It failed because of the complexity of the question. If the children had been asked distinct questions for each of the four vegetables, there would likely be far less confusion.
TE is asking the right question. You have to design questions that most test takers should be able to try to answer. If a large % of a test population fail to understand a question that covers standard curriculum material, it generally points to a bad question.
bernie, weren’t you an attorney? It’s a nice thing to be retired and still have children in school. I know that I’m going to have to work well into my 70s to support mine. I had no idea that my public service job would not yield me the luxuries that the politicians claim I have! In all seriousness, it’s great that you care enough to be part if the dialogue even in your retirement.
I agree that people should not jump to conclusions without evidence, just as the people who make these test questions should not jump to the following incorrect conclusions:
1) Only the children who answer the question correctly have the knowledge and skills that the question is supposed to measure.
2) The teachers of children who miss this question are of poor quality. 3) The test makers have the authority on determining who knows what and how this will be measured but will not take the responsibility for the invalidity of their own ill-prepared questions and the developmental inappropriateness of the work load required to answer them.
Lots of assumptions are being made in the reform movement that have fueled ridiculous questions like the one presented here for math. According to the test makers, it’s ok to make assumptions, but it’s not ok when experienced, educated teaching professionals see through this nonsense and then protest it. They are instead accused of “defending the status quo” of “failing schools” or taking a stance against teacher quality. They are called a special interest group, a political thuggery, drug mules and lazy, overpaid public teat-suckers. No matter what good intentions the first animal preservationists had, they still poked an angry bear or two. The reformist lexicon of insulting references for public school teachers has created some very angry bears.
I believe you are trying to be fair by thinking critically. Yours seems to be a “Devil’s Advocate” POV, but the background of many posters here suggests that some have experiential knowledge that others do not. You may have unwittingly poked some of us, but know that we are tired of being poked on purpose.
LG:
I appreciate your civility.
I am not an attorney. My children are grown. I was a management consultant in HR and I designed and analyzed all kinds of employee surveys, assessment instruments as well as performance management, selection and recruitment processes and professional development programs for primarily large private and public organizations. In addition, as the chief financial officer for my firm, I was responsible for decisions around pensions and benefits and our own compensation plan. (I have said all this before.)
I have had a longstanding interest in education, particularly higher ed due to my work in designing college recruitment processes for some very large firms and for labor market analysis for the NSF.
I appreciate that folks have experience in their fields. However, I do not trust arguments from authority or experience. For me, such skepticism is a fundamental tenet of critical thinking. I also do not think much of ad hominem attacks or those who make them: They simply increase my skepticism and motivate me to dig deeper.
Bernie, a “psychometrician” might think he was measuring worthwhile attributes, and he would just look for questions different proportions of children could answer, and thus be able to rank the children’s knowledge.
Then, one of them could come along and maintain that those “measures” should drive instruction of the children, and teachers and children must be held accountable to them. Entrepreneur “psychometricians” could devise many ways to jump on that, and compel teachers to go along. They could take over management contracts for whole schools, and hire each other as consultants.
So, the best spin I can see on it is, you’re gratified to see your own field used as a decisive source of authority, to cloak the whole scam. Measurement isn’t teaching, though, even if we could measure a child’s college readiness or competitiveness on the international labor market at age 8.
chemtchr:
Why on earth would I have any stake in what those designing tests do or do not do? Such comments make no sense. When the evidence was presented that this terrible question was developed by a test publisher, I was surprised at the level of incompetence and said so. What more should somebody do?
You said “Measurement isn’t teaching,” Who actually asserted that it was?
OMG. Well done, teachingeconomist. I had to stop and revise all the judgments I was making about you a few seconds ago, there where you nattered, “By most, do you mean 51% or a supermajority?”
Maybe you do really think, after all. If you only will.
Please, please, just go read some of Piaget’s work. Any of his observational studies will do. He moved away from his specific timetable of “stages” in his later work, but he devoted so much careful observation and clear thought to the actual attainment of mathematical fluency by human children, it’s a crime to throw his work away through simple ignorance of it.
Chemtchr,
As someone who has read Piaget on the age appropriateness of various concepts in mathamatics, perhaps you could offer an answer to my questions:
What percentage of students in a grade must be able to work with a mathmatical concept for it to be considered age appropriate and
At what age does age appropriateness cease to be a useful idea in mathmatics education?
Teachingeconomist,
The question isn’t about “what percentage of children” can “work with a concept”. It’s about whether children can be compelled to answer questions designed by an ignorant fool. The idea that an “advanced” child would just be a little grownup sooner is deeply idiotic. Children have a different way of working with concepts. It’s an area of serious study, and corporate education reform is busy attacking the very people who study it seriously, in our schools of education. No standardized test is going to determine whether an eight year old is on track for college.
The children Piaget studied turned out to by a non-representational study group, possibly because they’d spent so much time playing block games with delightful French psychologists. He thought children moved from a stage he characterized as “concrete operations” to “abstract operations” around the age of twelve. He was dismayed when examination of Oxford freshmen revealed that a great many of them had not attained that level.
Studies I find credible report that ability tracking before age 15 is disastrous for all children. It’s clear that the children grouped as “lower” might be deprived of opportunity and stimulation, but I think also that the ill-conceived straight-jacket placed on the advanced group hurts their development.
As for the gifted, we should feed their hearts and souls, and give them delightful and stimulating concrete and abstract experiences to challenge (but also follow) the neurological miracle that is already unfolding in their developmental sequence, just like we should all other children. And please, don’t hurt them.
It seems likely that the “ignorant fool” who wrote the question we are discussing here would write poor questions no matter what set of standards are being used in Tennessee.
Given that the most serious criticism of the CCSS is that they are not age appropriate, it seems important that the concept of “age appropriateness” be carefully examined and understood. I am not even sure that age appropriateness has a lot of meaning when standards are constructed for grade levels, and students in the same grade can be a year older or younger than their classmates.
I have to disagree with you about tracking before 15 based on evidence from my own household. My foster son did not successfully pass algebra 1 as an 18 year old high school senior, my middle son did very well in a graduate mathematics class (and a two semester P-Chem class) as a 16 year old high school senior. I think it would have been a huge mistake to have both of them in the same class at 14.
So much for reaching out. The CCSS hurts children, and was imposed on unwilling children, parents, and teachers by corruption and stealth.
You recommend that age appropriateness be understood, in the passive voice. I recommended that you investigate it yourself, because there’s a rich and complex literature. The Common Core displays its architects’ indifference to child development, but there is no reason under any circumstances to allow any faction to demand that children be held accountable to their business program by force of law. If your agenda is just to impose it anyway, you’ll say anything, and brush off anything, to argue for it. Public record of foundation gifts, alone. illustrates that there’s a whole industry of hired “advocates” who will do that regardless of what children, parents or teachers argue.
So we will just have to stop it by public action, whether its proponents like that or not. That means vote political hacks out of office, sue for public disclosure of self-dealing in public documents and emails, oppose lobbyist’s corrupt relations with legislators , and opt our children out.
Over and out.
I have no doubt it is rich and complex, that is why I am concerned with the criticism of the CCSS as being age inappropriate without any discussion of what age inappropriate means.
Perhaps this is something that might be asked the next time that is given as a criticism of some aspects of the CCSS.
I teach 5th grade, after teaching 6th for 10 years, and this problem is a piece of cake. Took two minutes. No big deal. Problem is asking if you know the various multiples of the 3 numbers, 24 radishes = 2×12, 3×8 and 4 x 6; 16 lettuce = 2 x 8 or 4 x 4; tomatoes have to go 5 x 5. Why all the excitement?
Because it was given to a third grader.
Apparently not as easy as you think. That’s what happens when you rush. There are sixteen combinations based on the wording in this item. See, it even confused you.
You mean factors
I think the wording implies more than straight factoring. If an 8 year old with uncommon critical thinking skills were to claim that her vegetable stand could display three rows of eight OR eight rows of three – that these are in fact two different ways to arrange them.
To NY Teacher
8 and 3 are not multiples of 24.nor is 4 or 6 or 3 or 8
I understand exactly what the question is asking….
2 rows..12
12 rows of 2
3 rows of 8
8 rows of 3
4 rows pf 6
6 rows of 4
24 is a multiple of 2,3,4,6,12…etc..
Same with 16..is a multiple of the numbers 2,4,8..not the other way
Thanks.
Discussion related to age equivalent or grade equivalent scores becomes an issue if students are performing poorly in 3rd grade, teachers keep providing interventions, a referral for psych. testing is agreed upon to pursue eligibility for sp.ed. Problem, the grade equiv. scores and age equivalent.scores may be at grade level, intellectual functioning within normal range, no evidence of processing deficits, and no disability issues can be substantiated because the expectations of the CCSS are so far out of line with age/grade level equivalency scores and expectations. No disability. Only Death by CCSS.
CCSS and testing insanity is criminal, unethical and immoral!
This is why parents of students in special education should file lawsuits as their childrens’ right are in violation. IDEA states that students have the right to free and appropriate education. While it still may be free; it sure isn’t appropriate.
Don’t forget 24 rows of 1. The question does not exclude having 1 in a row, only that there be more than 2 rows. Where’s my gold star?
Array – Items (such as objects, numbers, etc.) arranged in rows and columns.
Arrays
24 x 1
24 rows 1 column
1 by 24
1 row 24 columns
However, the question states:
“He plans to put each kind of vegetable in at least 2 rows. ”
so neither the 1 x 24 nor the 24 x 1 will work for this problem
Why, is the definition of a row have more than 1? I think a row can have zero in it. Certainly in a matrix, or an array, or a rectangle, or a grid, a row can have 1. So I’m going with 20 possible correct combinations. But it is semantics.
I don’t agree with the part about he wants to put them in groups and put them in sets. That implies doing two things, when in fact it is doing one thing, so I believe the word “and” is incorrect.
TC
The question says
“He plans to put each kind of vegetable in at least 2 Rows”
A row can have zero vegetables but if you have zero(no) rows then the row can not contain vegetables because the row does not exist.
Still say they’re messin’ with the kids’ heads.
Funny!
Easton has been raising vegetables in his garden all summer. He plans to sell some of his vegetables at a local farmer’s market.
“He has selected 24 radishes, 30 onions, 16 heads of lettuce and 25 tomatoes to sell. He wants to display the radishes together, the onions together, the lettuce together, and the tomatoes together, and to place them in sets with equal rows for each kind of vegetable.
“He plans to put each kind of vegetable in at least 2 rows. FOR EXAMPLE, EASTON CAN ARRANGE 24 RADISHES INTO FOUR ROWS OF SIX (EQUATION: 4 X 6 = 24)NOW show ALL the different ways that he can display equal rows for each kind of the vegetables at the market. Write an equation for each way you find.”
An absolutely horrendous question for 8 year olds – especially kids with limited parental support. However if the item writer simply added ONE EXAMPLE as I have, it would have been much easier for a student to complete all the factoring required. Still a pretty convoluted way to ask an 8 year old if they can factor four different numbers. Without the EXAMPLE its very hard to understand what is meant by an “equation”. The term “equation” is not even the proper terminology for a factoring problem. This example is typical of the obtuse wording that confuses and frustrates most students – but that CC item writers are apparently using to create quasi-rigor. Totally bogus.
The vague and confusing syntax turns this problem into a bad reading comprehension question. Makes me wonder if Sarah Palin is now working as an item writer .
Most students need to be guided to an expected response with very clear and specific wording and examples. Vague or confusing questions lead to lots of “IDK”s.
Too Funny!!!!! 🙂
Asking an 8 year old to “show ALL” of the SIXTEEN different combinations along with equations is another aspect of this item that is beyond reasonable
Agree Totally
i thought that there was supposed to be a relationship among the groups of vegetables, so I was totally confused about the task. I suspect most kids would feel that there was supposed to be some pattern/relationship among the numbers. This distracted me ( and would distract them) from the actual factoring problem. BTW I teach second grade.
Apparently, that’s the test writer’s goal: distract the test taker into failure!
True!!!!
If I were teaching this problem…
I would use real radishes-onions-lettuce, and tomatoes..
I would make the school buy these items…
24 radishes, 30 onions, 16 heads of lettuce and 25 tomatoes
Bill = $$$..( I would use leaf lettuce)( I would use green stalk onions)
I would then take it home and carefully cut up the vegetables..
I would then bring it to school the next day in separate containers….and make a salad bar..
I would then have the children figure out how many salads we could make from the vegetables..
*******************************
I would then have the school to buy me garden soil and the above vegetables….(which should have been done before this problem)
I would divide the class into 4 groups..
Yep..You guessed it…Radish-Onions-Lettuce-Tomato.
Each child in each group would plant a vegetable..
Each child would measure the growth each week…
Each child would make a Table of Values
x = number of weeks…y = height of plant
Each child would graph on a coordinate plane the growth each week..
Each child’s graph would then be displayed on the wall with a picture of the vegetable..
Each child would …when the vegetable matures ….connect the dots.on their graph.to see a linear relationship.(unless you mistakenly planted the “Jack in the Beanstalk Beans)
Each child would then figure out the Growth Rate by counting the vertical change and the horizontal change..
Each child would then compare the growth rate of each vegetable
1 inch per week……..etc….or use cm growth..
Each child would then write an equation in y = mx + b form..
.where b is 0 as we started with a seed….so y = mx…
My onion grew approximately 2 inches per week so my equation is
The height of the onion grows 2 inches per week
So……….y(the height of the onion) = 2 times x(the number of weeks)
Now we will write a recursive equation…
Recursion-a process in which each step of of a pattern is dependent on the step or steps that come before it.
Next = Now + 2 starting at 0
Next week’s height is going to equal this week’s height + 2
(assuming you take care of your plant and it continues it’s constant growth)
However..I would have first had the children to compare their own tables and their graphs so they could see the pattern from week to week..
Height increases 2 inches per week……we have an Arithmetic Sequence…….
Let us write a Next-Now recursive….
Then we write the linear equation of the line that goes through the points..(after connecting the points)..
Now we forgot to do research on these vegetables…
Do we have the right climate to grow these vegetables?
What temperature is need to grow our vegetables?
What kind of soil do we need.?
How much sun does each plant need?
How often do we water them?
Can we leave the plants in the room or do we need to take them home over the weekend?
Who introduced these vegetables into the US?
Did they first come from Spain or Africa or the Native Americans?
Who were the first Europeans to come to America?
When?
How long before they brought over the vegetables?
Ok children
You must learn to draw these vegetables in your Art Class
You must learn how to grow these vegetables in your Science class
You must learn the origin of these vegetables in your History class.
You must learn to write a recursive and an explicit equation for the growth rate of these vegetables in your Math Class
and learn how to write an Arithmetic Sequence from your data..
Please note that x – the number of the term and y = the value of that term
You must learn to make a salad in your Foods Class
You must learn the nutritional value of these vegetables in your Health Class….along with Caloric intake etc..
Let’s see.
Third Graders……I am your Teacher
Art-Science-History-Math-Foods-Health and Nutrition
Time for class change..Oops forgot none in third grade..
OOps..Sorry kids..it is June….Have a Nice summer !!
And by all means…make sure you listen to some music..
So sorry we had to leave that out…
But this question is more important…
Please have your parents teach you how to
Add-Subtract-and learn your Multiplication Tables this summer…
Now to improve your constructed response item Neanderthal, just feed it into the Sarah Palin on-line, syntax translator.
lol
I would patent that invention if I were you….
Brilliant!!! Love it!
I have written over 2000 questions for various companies..
This was not a constructed response question.
It was actually meant to show that the question is an entire week or more worth of lessons…
I still write questions..but for myself..not for any company…
Chemteacher~
Bunker Video of Hitler is chilling. Either way!
We are at a point in our educational malpractice era that we do need to think about a Day of Reckoning, harm done to all, long-term destruction…from forcing kids to survive psychological torture, families under siege, invasion of privacy, stolen confidentiality, future harm of EVERYONE having access to confidential data, screwing up all normative data, losing compass of typical expectations related to child development, mental health….the list is endless!
Responsibility for this will come.
Taking way too long.
Evil must ALWAYS have an END.
Wouldn’t it just be so much simpler to ask, “What are the factors of …?” That is essentially the concept this problem is covering, which should only be taught once the times tables are memorized. The type of inferencing this problem requires is too murky for 8 year olds. If I were that parent, I would let my child design (in color, of course) and cut out veggie manipulatives and paste them on the homework packet. Then write out on the bottom of each beautiful, orderly design the following: 24 is 2×12, 3×8, 4×6, etc.
The beauty of arithmetic is totally destroyed if you don’t let children see the rhythmic order in each pattern/table. That’s what 8 year olds should be learning, in a variety of ways. Once that foundation is built and a child developmentally comes into his own as the independent-problem-solver-who-doesn’t-need-grown-ups-thank-you-very-much, then you give them the problems that stump. If you bring math (not the same as arithmetic) too early, you undermine your role as a teacher to reveal amazing things about the universe. After all, your role is to author their education, not make them feel bad about themselves. Force-feeding concepts concepts too early can create a disinterested and or fearful child of following through anything that seems difficult.
Some children are really advanced and can just inhale this information, and have families backing this inherently competitive behavior. It always seems like there is “work” to be done elsewhere, perhaps in the social realm, if not in other rudimentary subjects. Just saying…
Not just ask what are the factors of for an 8 year old..
This question needs to deal with only one vegetable…to begin with..
Let us say you have 24 blue buttons instead or blue disks or bottle caps…etc…
1. Teacher takes 8 buttons and arranges them in
A.. 2 Rows of 4
* * * *
* * * *
How many Rows do we have in this model? 2
How many buttons are in each Row? 4
We can say 4 + 4 = 8
We have 2 groups of ___(4’s.).We can see that equals ___(.8)
We can say 2 x 4 = 8
B.. 4 Rows of 2
* *
* *
* *
* *
How many Rows do we have in this model? 4
How many buttons are in each Row? 2
We can say 2 + 2 + 2 + 2 = 8
We have 4 groups of ____2’s..We can see that equals ___*
We can say 4 x 2 = 8
Teacher then gives students 12 buttons
A. Asks students to make 2 equal rows
Asks above questions..(students need chart or handout to fill in)
Students result will be 2 x 6 = 12
B..Asks students to make 3 equal rows.
Same instructions as above
C. Asks student to make 4 equal rows
Same instructions as above
D. Asks students to make 5 equal rows….hmmmmmm..why?
Same instructions as above
E Asks students to make 6 equal rows..
Same instructions as above
F. Write all equations..come to the old fashion board or hold up a card ..Let’s compare..and share…
Which equations use the same numbers but are in a different
order?
HW could be 20 buttons or bottle caps or they could draw etc..
I am positively sure that 3rd grade teachers know perfectly well how to model multiplication tables such as the above
………..without using Smelly onions…Buggy lettuce…Squishy Tomatoes…and Rabbit Radishes
Elementary teachers are the most creative teachers on the planet and would most likely put my plan to shame…
And.. I will also bet that by the time they finished their math lessons..students would understand the concept of multiplication and be able to learn their multiplication tables with ease….and understand the relationship between multiplication and addition .
When the creative 3rd grade teachers finish with this they would be easing in word problems….one right after another in daily review capsules…adding a wee bit more each day..
Building on a SOLID FOUNDATION…..instead of throwing it at them to see what sticks the way the CCSS is h*ll bent on doing at the expense of a child’s education!!
SICK OF CCSS
The last dang time I looked at the construction of anything..
It either has a FOUNDATION and a FRAME!!!!
Pedagogy…this anger is not directed towards you…but because of the Big Pile of Mess they are throwing at these children so the Test Scores will win them another election or yield the Giant Companies more money than God!!
Correction:
It either has a Foundation or a Frame or both
Nobody has pointed out that in the real world this question makes almost no sense. Radishes are usually sold and displayed in bunches to keep them from during out and looking and tasting bad (an important physics topic in its own right)
Also
gfbrandenburg
You are exactly right!!!!!!
I guess they put the bunches in rows…but most buy them in a bag anyway.,.
I shared this with a 3rd grade teacher, along with my
confusion about what the heck the expected solution was, and she
informed me that this is typical and simple for 3rd graders, as a
follow-on to prep work about working with arrays. So I guess if
you’re a 3rd grader in a current 3rd grade class, this kind of
stuff is straightforward. If you’re an adult trying to understand
this word problem in isolation, it makes no sense.
Great
A farmer has 8 tomatoes and 12 apples he wants to sell at the Farmer’s Market.
He wants to display his tomatoes in at least two rows.
His choices are
2 equal rows of 4 because 2 x 4 = 8
4 equal rows of 2 because 4 x 2 = 8
Write an equation for each of the choices the farmer has for displaying his
12 apples in at least two rows.