Thoughts and ideas on improving math education in NYC and what parents can do.
The term new math has been commonly used to denote the new ways in which the common core standards have suggested to teachers and administrators how math should be taught. New math can be seen by someone looking from the outside as a dark cloak of information unknown to anyone except the teacher, and conceptually too challenging for parents to help teach to their children. New math would seem to erase everything that parents know about math and leaves them incapable of being a part of the process of teaching mathematical concepts to their child.
The truth is, there is no such thing as new math just as there is no such thing as old math. The fundamentals of math do not change over time. 2 + 2 = 4 was true in 1865 and its true in 2022. 4 x 2 = 8 was true in times past and will hold true till the end of time. The cloak that some have tried to put over math needs to be removed and thrown away. Math is not a mystery with its secrets known to just to a few, and the experiences and knowledge of parents and older generations are just as germane and valuable today as they have ever been. Math also allows for a myriad of approaches to a sound and correct answer. Denying students the option of using sound and accurate practices from earlier generations does a disservice to the concept of mathematical fluency and differentiated learning and needs to discontinued.
What has changed over time are the mathematical standards that govern what a student “should” know and be able to do at a certain grade level. What has also changed is how some of these things are being currently taught. With a new set of standards coming in soon (Next Generation), we will see another shift. The objective behind these new teaching approaches was to increase understanding by mastering mathematical concepts and applications which in turn would increase fluency amongst students. The argument was that the old approaches relied too much on rote memorization. Apparently, students didn’t truly “understand” why 9 x 8 was equal to 72. So instead of “knowing” what 11 x 12 equals, students are expected to continuously figure it out through a teacher taught algorithm. Memorization is antiquated and does not lead to conceptual understanding is what we are told. Based on what I have observed in the years working with students that come to CAS Prep, this experiment is not working. If anything, students are more disconnected from mathematical fundamentals than ever before. Students seem unaware of fact families and the connections between numbers. Students have no idea what mathematical operations truly “do.” When should I multiply vs when should I divide? Word problems end up being nothing more than experiments in guessing.
The following are some of the current practices that I feel are holding our children back. The first is the argument against memorization. The human brain is capable of memorizing millions of bits of information. Think of these bits as math facts. The more math facts a child has memorized, the more time that child has to process questions that require utilization of those facts. A high school student trying to factor a quadratic equation needs to know the factors of a given number. Using an algorithm to figure it out then factoring wastes time and creates more problems than solutions. Memorization is vital and important; it just needs to come with understanding.
The second is the argument against memorization and utilization of the times table. It pains me to see students in 5th grade trying to figure out 9 x 6 using a table instead of “knowing” the answer. Multiplication tables provide students with an understanding of multiples, factors, equivalent fractions, division and so much more. The fact that they are no longer taught is a disservice to our children. We are forcing our children into a world of calculating simple facts as opposed to using simple facts to solve complex problems.
The final argument I want to address is against the teaching of vertical multiplication and long division (as most people/parents have learned it). While I agree that I have seen many ingenious and approaches to these operations in my time, specifically those coming from Eastern cultures, unfortunately, that is not what our students are being taught. In division for example, the thought that guessing ANY number a multiple of times until you finally arrive at a solution may be fine for some early learners struggling with the concept, but I’ve encountered many 4th grade students who are ready for long division, right now. Long division amongst other things, teaches estimation of values, strengthens multiplication skills, and inherently builds an understanding of what the division operation actually does! Students do not need to have the process parceled out over a 4-year sequence (which using a probability model leads to failure amongst the majority of students).
So, parents, in conclusion, what you know is NOT obsolete. Math facts are crucial and important. Flashcards (in actual or digital form) are incredibly efficient at building basic facts that students should know, as opposed to figuring them out. Multiplication tables are great, but be creative about how you build and use them. Yes, filling out a 10×10 or 12 x 12 or even 15 x 15 array may not be the exciting thing for a child to do but if you spruce it up some you’ll end up with a 3rd grader that “knows’’ her/his multiplication tables up to whatever you deem appropriate. Not only that but you can extend its use so that your student will also be able to list the first 8 multiples of 8 and all the whole number factors of 48 (among other basic facts). Finally, believe in the power of long multiplication and long division and teach it to your child. When he/she is in Algebra 2 using long division to divide polynomials or vertical multiplication to multiply a 3-term polynomial by a 5-term polynomial, they will come back and thank you. Scalability and efficiency are just as important as any other mathematical concept.
We are effectively limiting the successful trajectory of NYC students by the dismal record we have maintained as it regards to math education in NYC. The data as it pertains to state education measures continuously reflect the fact that most schools in communities of color have failing scores and their students are not performing at grade level. We have internally accepted this failure as a matter of fact and thereby limit our children’s access to the most powerful careers of tomorrow: technology, engineering, and computer science.
As the new administration, from the chancellor to the newly superintendents takes over in NYC, we have an opportunity to rework some of our approaches to what and how we are teaching our children. We have done some of this work in ELA, modifying the whole language concept and reinserting phonics and grammar back into the curriculum. We do not need another 10 years of failure to see that we need to modify math instruction as well. It is also incumbent on parents to reintroduce themselves into that conversation about math and the value of what they know. Your voice matters! New math needs lots of support and it is called old math!!
Sam Adewumi has been a coach, teacher, and educational leader for 20-plus years. His organization, CAS Prep (casprep.org) works with students all over NYC on test prep (SAT, SHSAT, State Assessments) and educational enrichment through an emphasis on teaching students fundamentals and effective strategies in both ELA and Math. He believes in the ability of our children to soar, given they are provided with the necessary tools, information, and support.