Kate Raymond of the University of Oklahoma challenges the claim by Mate Weirdl of the University of Tennessee that the Common Core is deeply flawed in the early grades.


As a mathematics educator, I was disturbed by recent comments made by Dr. Mate Wierdl on your blog site and felt the need to contact you to respond, educator to educator.

It is interesting to me that Dr. Wierdl ended this comment by saying he is not an expert on ELA; implying that he is an expert on the teaching and learning of mathematics. While Dr. Wierdl is a mathematics Ph.D., nowhere could I find any reference to education he has received or research he has done on teaching and learning.

Perhaps if he had such an education, he might have avoided some elementary mistakes he made in his critique of the common core. While I am by no means a proponent of, or an expert in, common core mathematics, the baseless and inaccurate assumptions Dr. Wierdl only serves to muddy the waters when it comes to a discussion of standards, curriculum and assessment in mathematics education. In large part, this is because Dr. Wierdl fails to distinguish between standards (which can generally be thought of as goals), curriculum (the experiences of students) and assessment (a measure of students’ understandings). Most fundamentally, Dr. Wierdl has conflated Common Core Standards with the standardized tests referred to in the article that compares Finland and the US. The tests referred to in that article were not written by the creators of common core, and the literature in mathematics education already documents that they are not well aligned with the intentions or the content of common core; the article itself references this problem when it speaks to the fact that Pearson, a for profit company, developed both textbooks series and standardized tests for the state of New York. So to critique the common core based on these tests is simply illegitimate.

More disturbing however, Dr. Wierdl makes several assumptions that, had he had an education in teaching and learning, he might have avoided. For example, he states that young children can intuitively understand the difference between 12 and 21. While I am sure this was intuitive for him as a young student, research shows that for the vast majority of students, this is not at all intuitive. Young children often see the difference between these two numbers as akin to something like * # verses # *.

Would you necessarily see these two as fundamentally differently? Would you intuitively know that one is larger than the other? As the article that Dr. Wierdl points out, students are just learning to read in grade one; that includes learning to read numbers. Many mathematics standards, including Finland’s, as it turns out, place an emphasis on “properties of numbers” and “the use of manipulatives to break down and assemble numbers” (language I quote from a description of the Finnish mathematics standards, see http://timssandpirls.bc.edu/timss2015/encyclopedia/countries/finland/the-mathematics-curriculum-in-primary-and-lower-secondary-grades/) in order to help students build a schema for understanding numbers. While many (but not all) students may be able to successfully add relatively small numbers without such a schema, those who do not begin to have difficulty in adding and/or multiplying large numbers. For example, if asked to add 3472 and 1248, students without such schema struggle to remember when to “carry” (or “borrow”, for subtraction), because they have not build the concept that 2 and 8 make one whole ten (so that they can carry a one to the tens place) or that that carried ten, the 70 in the first number and the 40 in the second number combine to be one whole hundred and two extra tens, so that a 2 should be placed in the tens column while a 1 is carried to the hundreds column.

The difficulties become even more pronounced when students are asked to multiply 54 times 19. I would imagine Dr. Wierdl, like many mathematicians, is fluent enough to understand that he can multiply this in a number of ways, including multiplying 54 by 20 (which is a much more simple problem due to the round number) and subtract 54 to get 1080-54= 1026, rather than a long step by step procedure which often makes very little sense to young children. I imagine that Dr. Wierdl finds such flexibility with numbers intuitive, but research shows most students do not. However, students’ ability to be flexible with numbers can be greatly improved if they learn to communicate mathematical thinking. Vygotsky’s social constructivist theories of learning have been proven time and again in mathematics education research; students learn by reflecting on their own thinking and the mathematical thinking of others. This is reflected in Common Core and other standards by emphasizing the development of students abilities to communicate mathematically, a skill by which Dr. Wierdl makes a living. However, contrary to Dr. Wierdl’s assertion, I challenge anyone to find a set of standards that requires students to “explain the difference every time they see it”.

Given all of that, I do agree that “fake” real life questions are a significant problem in US mathematics instruction. However, while standards promote application of mathematics to real problems, nowhere do the standards promote the use of contrived “fake” real life scenarios. Those scenarios are largely the result of textbooks (which are generally not developed by writers of standards) and teachers who do not have the educational background or mathematical strength to apply mathematics in more authentic and interesting ways. This is again a problem with the curriculum, not the standards, and one that is being addressed by many leading experts in mathematics education (see https://www.ted.com/talks/dan_meyer_math_curriculum_makeover, for example).

While I have a Master’s degree in mathematics, I would not presume to present myself as an expert in the field of mathematics. Since Dr. Wierdl has no background in education, I would respectfully ask that he do the same and that the community at large be wary of opinions put forth by ‘experts’ who have no background in teaching and learning.
Sincerely,
Dr. Kate Raymond

Kate Raymond, PhD
Department of Instructional Leadership and Academic Curriculum
Mathematics Education
University of Oklahoma
Jeannine Rainbolt College of Education
820 Van Vleet Oval, ECH 114
Norman, OK, 73071
kate.m.raymond@ou.edu