Thinking and Linking by Joanne Jacobs
Gene Expressions responds to Chris Correa’s assertion that Newton, Massachusetts isn’t teaching “anti-racist math” instead of good, old-fashioned math-type math.
Once again Massachusetts needs to be commended. Numbers CAN sometimes prove to be racist, neocolonialist, and/or counter-revolutionary. Around two weeks ago I witnessed a number 8 mumble a quasi-racist slur under its breath. However, the binary system seems to be more progressive. I’ve yet to see or hear anything racist from a one or a zero.
It’s hard to improve on what is written in Gene Expression, but here are my thoughts.
Chris Correa wrote:
“The so-called math wars are counterproductive. Characterizations of math education as NCTM -standard based vs. traditional or developing conceptual understanding vs. procedural understanding are simplified characterizations that don’t really help improve mathematics education.
If we linger with these simplified characterizations long enough, we dream up fantastical ideas that don’t exist in the real world, such as anti-racist math.”
Counterproductive? To whom? Educators and the status quo? Public education and NCTM have a monopoly and they decide on the curricula without outside input from mathematicians, scientists, and engineers. When these same professionals say that NCTM math is not adequate, it is called a “war” and criticisms are called counterproductive. These profesionals NEVER label it as a conflict between developing conceptual understanding vs. procedural understanding. This is a false dichotomy that is used by educators to bolster their position and confuse the issues. Educators will then talk about “balance”, as if the solution is somewhere in the middle, and, oh, by-the-way, they will decide what balance means.
Mathematicians say that the problem is that NCTM math wastes time, teaches the wrong things, sets low expectations, requires little or no mastery, and does not prepare students for a proper course in algebra by 8th or 9th grade. Forget constructivism and discovery learning for a moment and just look at exactly what problems NCTM math expects the students to know and master at the end of each grade. Also, look at standardized state math tests. These tests are trivial and good marks on these exams say nothing about whether schools are preparing their students properly for technical careers. These minimal tests now set the maximum standard in public schools.
Anti-racist math might sound over-the-top, but it is part of the philosophy that influences NCTM math curricula. It shows up as lower expectations. The NCTM does not want math to act as a filter or “computational gate” for women and minorities. Removing this gate is a major factor in the NCTM change in how math is defined, how it is taught, and the grade-by-grade expectations (or lack thereof). Everyday Math is specifically designed as a year-to-year spiraling curriculum so that if a student doesn’t understand the material in one grade, he/she will see it again in the next. This means that any level of success depends on how EM is supplemented with mastery drills and how the school deals with social promotion. However, there still are problems with the lack of content and preparation for a proper course in algebra. This shows up as the K-8 to high school curriculum gap. NCTM math does not properly prepare students for college prep or honors math in high school without outside help at home or with tutoring.
EVEN IF a school improves year-to-year, that is only relative. Remember that state educators select the tests and set the pass/fail ratings. You have to look at the absolute. Look at the actual problems. Look at the tests. Look at the grade-by-grade expectations. Compare them with the California Math standards.
Do you think the standards themselves prohibit a quality curriculum? Or are the standards simply vague enough that they allow for really weak implementations?
Chris C. wrote:
>”Do you think the standards themselves prohibit a quality curriculum? Or are the standards simply vague enough that they allow for really weak implementations?”
Yes, current math standards and frameworks make it impossible to select a quality math curriculum. Imagine how difficult it would be in Newton for parents and/or some teachers to implement Singapore or Saxon math. (I bet some educator would raise the issue of filter or computational gate.) Of course, the schools would argue that these are not quality curricula. Educators (with very little knowledge of math) decide on curricula based on their own educational philosophy and don’t want any outside help, even from mathematicians, scientists, and engineers.
Standards themselves can also prohibit a quality education. Everything is standards-based and test driven nowadays. These standards and tests are very weak and everyone is focused on improving the results of these tests – slow progress towards a minimal goal. Do you think that improving the lowest common denominator is providing a quality education even though the curriculum might make it impossible for students to have a career in math, science, or engineering? I believe in the best educational opportunities for each individual child, not the best lowest common denominator average for all students. Many schools use the test results to lump together the exceeding expectation group with the meeting expectation group to see how well they are doing – even though meeting expectations is set very low. Small, relative improvements don’t mean much for an inadequate curriculum.
There are standards and there are frameworks and I haven’t seen any consistency in how each is defined execpt that in our state, the framework is a philosophical guideline and overview of content defined on the state level, whereas the specific grade-by-grade standards are defined at the school district level. This has to do with the town’s control over their own curricula. There are changes going on now where the state educators and politicians want to exert more control to create a specific state-wide grade-by-grade curriculum. In exchange for this loss of control, the state is talking about revamping how education is funded. That is a different issue.
For example, our state’s framework definition of math is:
“Mathematics has been defined in a myriad of ways. Entire books have been written that strive to define the discipline of mathematics. For our purposes in this framework, readers should consider the definition of (Math) to be the study of patterns and relations, with people interacting with each other and the physical world as they explore the process of thought, solve problems, make connections, reason, and communicate ideas.”
There is not a lot of math in this statement. It also says the following:
“A framework provides a vision for mathematics programs. It is a document that guides the creation, selection, and implementation of effective programs designed to meet the specific needs of individual districts, schools, classrooms, and students.”
Philosophy is a major driving factor in the selection and implementation of the specific curriculum. For math, that means that it has to be NCTM math.
The framework also says:
“Underlying each report calling for reform in mathematics education to meet the demands of a changing world, is the belief that all students can learn mathematics and achieve high standards. The National Council of Teachers of Mathematics consistently uses the term “all students” throughout its curriculum and evaluation standards. The selection of this terminology was deliberate …”
All students CAN LEARN. However, it glosses over the problem that all students learn at different rates. Also, part of the modern philosophy of education is the idea that all kids of the same age need to be taught in common mixed-ability groups. Our superintendent knows that this is a problem, but insists that there will be no tracking or pull-out, even in 7th and 8th grade. Period. Well, due to strong parental complaints, they do allow some kids to study pseudo-real algebra in 8th grade along with the CMP material, but not for a complete year. Our schools talk about differentiated instruction, but this usually ends up as enrichment done as homework.
Educational philosophy drives everything. Schools want to treat all kids the same, but they are not the same. They say that they want to use differentiated instruction, but they really don’t know how to do this. The mantra of “all students can learn” means that the content coverage is lowered and grade-by-grade expectations are lowered using spiraling and social promotion.
Standards define the content that is covered year to year and it is impossible to cover more material, even for the better students. Enrichment is used rather than curriculum acceleration. If the standard is low, then of course the standards themselves prohibit a quality education. Standards can be implemented weakly, whether or not they are vague, but it is virtually impossible to see schools expect more than what the standards specify.
Philosophy drives the selection of the specific math program that is used, but there is some leeway in how these curricula are implemented. Some NCTM math programs can be improved locally up to a point, but others are beyond help. Many schools choose EM becasue it is the best of the NCTM lot (or, of the worst, I should say). Then, they add mastery drills and increase grade-by-grade expectations. This helps, but, you really cannot change the fundamental philosophy of EM – the rapid spiraling approach and the pedagogically-obstinate, arbitrarily different approach to basic algorithms. There still is a content and skills gap that has to bridged to get to college prep and honors math in high school.
In the end, the Math Wars is all about lower versus higher expectations and coverage of material. If a curriculum doesn’t cover the needed material, it is extremely unlikely that the school will make up the difference. K-8 educators cannot redefine math for their own philosophical and pedagogical agenda without regard to where it leaves the kids in 9th grade.
“Yes, current math standards and frameworks make it impossible to select a quality math curriculum. Imagine how difficult it would be in Newton for parents and/or some teachers to implement Singapore or Saxon math…”
Newton uses McDougal’s algebra text in 7th snd 8th grade. I hear the content in these texts is quite good (i haven’t looked at them myself), and Newton’s tenth graders are among the best in the state in mathematics (over 80% proficient).
>”Newton uses McDougal’s algebra text in 7th snd 8th grade. I hear the content in these texts is quite good (i haven’t looked at them myself), and Newton’s tenth graders are among the best in the state in mathematics (over 80% proficient).”
We all know what “proficient” means when it comes to state expectations – low! Look at the exam questions and how they define “proficient”. How many of these kids are taking college prep or honors math”? How many of these kids received outside help at home or with tutors?
From the original article:
“The school department offered no tangible explanation for these declining scores other than to admit that they have no explanation, as articulated by Assistant Superintendent for Curriculum and Instruction Carolyn Wyatt (salary $106,804), “[The results] have decreased, incrementally, each year and continue to puzzle us.” She went on to admit that this downward trend is peculiar to Newton and “is not being seen statewide.” Again, she offered no explanation, but she did assure the School Committee that her assistant, Math Coordinator Mary Eich (salary $101,399), is currently investigating the problem.”
Are you now arguing that there is no problem in Newton? Everything is really fine because 80 percent of Newton’s tenth graders are “proficient” in math. Are you saying this will be true when the current crop of kids get to tenth grade? Nice try.
Are you hoping that any problems that do exist are the fault of implementation and not the curriculum, standards, or educational philosophy? You never addressed my previous comments. The best you can do is try to say that there really isn’t a problem.
It’s good that Newton starts tracking kids based on ability in math starting in seventh grade. This should help, but how many are properly prepared for high school college prep and honors math? Your 80 percent proficient in tenth grade is meaningless. Tracking, however, is not done in our schools and in many other schools around the country. This is a philosophical decision. You were the one who brought up the topic of Math Wars. You cannot now talk only about Newton.
As for McDougal Littell’s texts, it depends on exactly which ones you are talking about. There is no mention anymore of “Gateways” on their web site. One text: Algebra 1: Explorations and Applications (not available anymore?) was rated poorly (2.2 out of 5.0).
The only texts they have which are rated well are the ones called: “Concepts and Skills” and “Structure and Method” which have been approved in California for their rigorous math curriculum. (Now called the California Middle School Mathematics Concepts and Skills series). I don’t think this is what Newton is using.
“Are you now arguing that there is no problem in Newton? Everything is really fine because 80 percent of Newton’s tenth graders are “proficient” in math.”
I am skeptical.
1) The original writer clearly misrepresented MCAS data, ignored changes in the school’s demographic characteristics, and deceptively applied curriculum statements about History to mathematics in an effort to conjure up this “anti-racist math” problem. These practices make me skeptical of his claims.
Should they not?
2) The test scores themsleves do not indicate a huge problem with curriculum in Newton. First, 2001 was clearly an outlier year. Second, Newton’s 4th, 8th, and 10th graders are doing quite well. If there was a systemic issue with an math-less “anti-racist curriculum” wouldn’t we see the effects in more than one class of students?
Please keep in mind I’m not interested in defending NCTM standards or multiculturalism in schools. I never have been. I just wish people could get beyond simplistic characterizations of math programs such as “anti-racist math”, “drill-and-kill math,” or whatever.
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