not worry about your difficulties in Mathematics. I can assure you
mine are still greater.”
A friend of mine sent me a YouTube video comparing common core math with “old math.”
My first thought was this is the dumbest thing I have ever seen. Now let’s be clear my reaction was not because the old math was so much faster. After all, the person doing the old math is merely solving an equation. The teacher is instructing the students in a common core mathematics process which takes longer. So it was not the length, it seems to me that the process is complicated, off track, and fails in several cognitive theories.
However, I believe in letting the research speak for itself, which means double checking your opinions with the literature. Most of my work is at the college and university level with a focus on STEM education. So what effect has the common core had on college students, primarily STEM students?
Before we look at the effect of the common core standards lets review what the common core is. The common core standers are a guideline of what students should learn each year of K-12 education. The standards are meant to be rigorous and meet the need of colleges and employers. According to the criteria for the working group, each standard should have:
“Goal: The standards as a whole must be essential, rigorous, clear, and specific, coherent, and internationally bench marked.
Essential: The standards must be reasonable in scope in defining the knowledge, and skills students should have to be ready to succeed in entry-level, credit-bearing, academic college courses, and in workforce training programs.”
The publishing of the full common core standards was in 2010. As of 2017, 46 states have adopted the common core standard to some degree. Eleven of the states have announced they are undertaking rewrites and changes to the standards.
Even with 11 states announcing rewrites or changes, this is still a high adoption rate. The adoption rate does not tell the whole picture. In K-12 education a lot is left up to the local school districts. While states have adopted the standards, it is not clear how consistent implementation is. It will likely get even harder to study the common core standards, as many states are renaming and modifying the standards. Many of these changes may be cosmetic as Tom Loveless says:
“A lot of states have simply re-branded the standards, changing the name or slightly tinkering with them without making any great change in substance” Loveless says. “That to me suggests that it’s more a political response than anything else.” (Common Core no more? New York and 21 other states revise or rename K12 standards, District Administration, By Alison DeNisco | October 9, 2017, retrieved June 6, 2019, from https://districtadministration.com/common-core-no-more-new-york-and-21-other-states-revise-or-rename-k12-standards/)
How do teachers view the standards? According to a report by the Center for Educational policy: “Across the five focus groups, most elementary school teachers expressed positive views of the Common Core State Standards. … Teachers said the Common Core had changed instruction in positive ways, such as teaching for conceptual understanding and developing students’ thinking and problem-solving skills.” (Listening to and Learning from Teachers: A Summary of Focus Groups on the Common Core and Assessments Key Findings and Policy Recommendations, Center on Education Policy, By Diane Stark Rentner, Nancy Kober, Mathew Frizzell, and Maria Ferguson, October 12, 2016, Retrieved June 6, 2019, from https://www.cep-dc.org/cfcontent_file.cfm?Attachment=RentnerKoberFrizzellFerguson%5FSummary%5FListenLearnTeachers%5F10%2E12%2E16%2Epdf)
So why don’t I like the method of mathematics presented in the video? Let’s look at the steps the students are being asked to do when answering, 35 x 12. In the first step the students break the numbers down into their components 35 = 30 + 5 while 12 = 10 +2. Students then plug the numbers into a grid and multiplication is done by multiply the rows by the columns. The multiplication produces four numbers which are added to get the final answer.
I have heard several arguments about why this method is better. First, it teaches students how to manipulate numbers. Second, by breaking the numbers apart, it is easier for students to remember and do the math in their head. The grid is a rectangle some instructors use area equations to represent the multiplication, height x width = area. By using this representation, students get a feel for the real size of numbers.
While I agree learning to manipulate numbers is essential for students, I am not sure this method teaches students that. I think it is more likely that students are viewing this as a trick or formula. We know from research that students are good at plugging numbers into formulas without understanding what they mean. Just look up the original research on the Force Concept Inventory Test.
The idea that this method makes it easier to do in your head sounds intuitively correct. However, it might fall short of our research on how memory works. Again we know that working memory has a capacity limit (I wrote about it here).
So when multiplying 35 x 12 in your head, you have to remember two numbers. When you separate the numbers, you need to remember four numbers; 30, 5, 10, & 2. Additionally, as I do the math, I need to remember more numbers 30 * 10 = 300. I need to remember; 30, 5, 10, 2, & 300 additionally, I need to remember that 300 is different than the other four. Using this method, it is more likely that a student will run out of working memory.
Lastly, I have two problems with using the grid to represent the actual size of the number. There is a counter argument of numerals being symbols so we can deal with numbers that we can’t intuitively grasp. However, that is not the biggest problem; the real issue is transference. Transference is the ability of students to take the information they learned and use it in new situations. If students get to fixated on numbers representing fiscal shapes and physical quontites, they may have trouble with things that are difficult to see or understand.
So what does the research say about college students that were taught using the Common Core standards during their K-12 years? According to a 2016 study, there is disagreement about what math standards college students need. “Mathematics finding 4 indicates that although middle school and high school teachers generally agree about what mathematics skills are important to success in STEM courses and careers, college instructors or workforce respondents ascribed much less importance to those skills.” (ACT National Curriculum Survey 2016, ACT, Inc, retrieved June 6, 2019, from http://www.act.org/content/act/en/research/reports/act-publications/national-curriculum-survey.html ) At least part of this discrepancy comes from colleges and universities have different views and requirements. The 2015 Brown Center Report on American Education (https://www.brookings.edu/research/2015-brown-center-report-on-american-education-how-well-are-american-students-learning/) shows small gains in student performance in states that fully implemented the common core standards. Unfortunately, these difference are below or borderline concerning statistical significance.
it appears there is not a lot of research, at least yet, on the
common core standards. What research exists seems to be leaning in
the direction of the standards not living up to its goal. Whether
this is the results of implementation or the standards themselves, it
is not clear. For the time being, I will have to live with my
dislike while trying to keep an open mind. What is defiantly clear
is that more research, mainly that focused on learning gains, is
desperately needed. Also, colleges and universities frantically need
to work with K-12 so that everyone knows what is the need and
expected of students perusing higher education.
Thanks for Listing to my Mussing
The Teaching Cyborg