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    • So… I have been stewing about this LA Times opinion piece for a few days now...


      My summary: Daniel T. Willingham feels it is a waste of time and money to improve teacher knowledge of mathematics--and seems to suggest that math is a “specialized” discipline that only some people can do.


      My friend, Sunil Singh (@Mathgarden ) posted a fiery response to this argument where he centered on the humanizing of mathematics that is currently happening in education settings.


      I would like to add to Sunil’s thoughts here.


      Dr. Willingham is misinformed about the real issues involved in mathematics teaching & learning in the elementary grades.  He is missing some key information in his piece-- the first major one being that the three competencies he boils maths down to  (memorizing math facts, knowing standards algorithms, & understanding those algorithms) really aren’t all that is important in mathematics. In fact those are just a TINY part of the awesomeness of mathematical thinking. 

      Dr. Willingham is subscribing to the view that mathematics is merely something we DO in the service of something else… in reality, mathematics is a way of processing the world-- we use mathematics to make sense of the world (and often to make it better!).  

      Dr. Willingham is focusing only a small subset of mathematics--which is perhaps the actual problem here.  He bemoans elementary teacher’s lack of understanding of the “whys” of math, without examining the causes of this-- We have in the US only been assessing his first two “competencies” for at least the past three decades. That has created multiple generations with only a limited view of mathematics- the kind that can easily be tested on a large scale, because those accountability regimes were what legislators and education funding folks cared about. 

      In short, we let poorly designed assessments dictate the currricula taught in schools. So much of what he is complaining about has been self inflicted. Most teachers have been teaching exactly what they were being asked to teach.

      What we have come to realize is that these tests aren’t really the metric we want them to be. We have discovered that it is really hard to drill mathematics down into the kinds of assessments we have time to give during school days.  

      So we have been shortchanging good math instruction in order to drill kids on the stuff for “the test.”  Real number sense takes time to develop, and we haven’t historically been giving students that time. Number sense is NOT memorization- it is developed in rich student experiences, and it is not easily measured by our current assessment/accountability systems.   

      Because… mathematics isn’t just a set of distinct competencies to be strung together.  But we have designed lots of math textbook series as if it is, and set up I-Do-We Do-You Do as a structure for how teaching should look.  We know better--this shortcuts student understanding-- but it sure makes textbooks easier to organize. Professional development won’t make a difference if we don’t give teachers opportunities to use it. Scripted textbooks leave little room for student discourse and time to wrestle with problem solving-- and that discourse is exactly what both students and teachers need. 

      I could forgive Dr. Willingham not knowing the nuances of this--they probably don’t discuss that much in psychology classes… but he inserted himself into the mathematics education discussion.  He is missing knowledge he needs to obtain before he makes the kinds of sweeping statements he made in his opinion piece. One way for that to happen is for him to peruse #MTBoS and #IteachMath hashtags on @Twitter.  He’ll get information on current research specific to mathematics teaching and links to some pretty amazing things happening in classrooms all over this country (& in others). He would find all sorts of evidence of the connections mathematics has to other subjects and disciplines. That is one of my favorite things about elementary education- teachers have more opportunities to make those connections, and students have the opportunity to notice them on their own as well.  Math doesn’t just live in math class!


      He could contact the National Council for Teachers of Mathematics (@NCTM) and have a real discussion about the state of elementary mathematics education-- and all the research and professional learning that is taking place. He would find lots of resources available to him about what students should be experiencing in elementary classrooms and ways mathematics educators are addressing the lack of coherence we previously permitted.  I do hope that Dr. Willingham will take some time to improve his own mathematics education knowledge before his next public statement writing off potentially a million teachers..

      Also, I just LOVE the idea of a psychology professor having the brilliant idea of just letting elementary teachers give into that fear he raised--like, "it's too hard for you to grasp, so we'll pay someone else to do that and you can do all the other stuff"-- as if everything should be siloed.  All the connection opportunities that get missed when we departmentalize... AND not dealing with the actual issue.

      His editorial "solution" isn't really one... to really break the cycle, we can't just bypass a generation of elementary teachers. We also can’t miss the fact that other caring adults have math anxiety as well--  do we really want to send the message to parents that only experts can do math? Don’t we want them as partners in this work?   

      We really can build numeracy across the board--elementary/middle/high/postsecondary/adult ed/public at large…and this is a real issue of equity.  Dr. Willingham doesn’t look at elementary mathematics from an equity lens at all in his opinion article, and that is a glaring omission.  He seems to be mostly focused on the test scores of US students, while ignoring the inequities in resources/materials available in elementary schools as well as the systems in place that actually hinder good teaching & learning. @ClearTheAir is one place he could go for some background and opportunities to learn about the systemic issues of equity in education. @NCTM has research and resources available for focusing conversations about equity in mathematics.   

      @DTWillingham has just today highlighted an article about getting knowledge delivered in PD to “stick” (https://journals.sagepub.com/doi/full/10.1177/0022487119886290) in order to bolster his argument that we should have math specialists teach all the math in elementary schools. . The authors of this study did a good job recognizing its limits in answering some of the questions they raised-- unfortunately, Dr. Willingham did not.  The study he references does not differentiate on type of PD, time of year it was delivered, how many hours or days teachers spent in the learning… and I imagine that those factors are variables that make a difference.  


      I would also point him to his own Twitter bio-- “One study is just one study, folks.”  YEP… and one opinion is just one opinion. There are many voices needed in the discussions happening about the direction of elementary mathematics education- I just want to make sure the voices that get elevated are not the ones arguing for hierarchies that produce more inequity.

    • One of the consequences of universal education is a warehouse, one size fits all approach to teaching. Wealthy people often provide their children with customized teaching. Home shcool parents can testify that different children acquire comprehension in different ways and that the technique which is successful in working with a first or second child may not be successful in dealing with a third or fourth child.

      One of the main problems in universal education is that theory focuses on large groups of students and statistical metrics rather than learning from the reformations of the past. "New Math" was introduced in the 1960s, just as I was beginning school. It was supposedly going to make the teaching of mathematics more effective that the teaching of the previous generation. It failed. No child left behind was supposed to resolve problems, it failed. The problem is that the focus is on "teaching" rather than "learning." Teachers needs to diagnose before they start prescribing. Most Arithmetic books that I have seen for large group teaching focuses on teaching as a large group activity rather than as a "coaching" type activity.

      Also, try as hard as you might, not everyone is going to be John Nash, John von Neumann, Alan Turing, or Albert Einstein. There will always be inequity of outcome. Even in the pursuit of equity in opportunity, unless a society made it illegal for wealthy people to hire tutors or pay for accelerated learning programs, it is not going to be achieved. There will always be a degree of inequality and all we can do is seek to provide those who currently have few opportunities with as many opportunities as we can.

    • Real number sense takes time to develop, and we haven’t historically been giving students that time. Number sense is NOT memorization- it is developed in rich student experiences, and it is not easily measured by our current assessment/accountability systems.

      I read the first few paragraphs of Willingham’s nonsense, started feeling depressed and so quickly moved on to @Mathgarden words of sanity to restore my hope that memorization isn’t the be all and end all of mathematics.

      It does take time to develop real number sense AND it’s not a primary focus of standardized assessments so it’s unsurprising that it doesn’t get developed. I think the need for exploration was brought up a lot in this year’s panel How to teach Higher Maths to young children, as well as last year’s panel How do you Make Maths Fun?

      I appreciate the work of both Sunil Singh and his co-author @cbrownlmath in attempting to bring to the classroom the exploration and joy that can be mathematics. If only the reporting of math education wasn’t stuck in the misguided past.

    • More from @Mathgarden on equity in math education:

      It is a lifetime endeavor of learning and reflecting. That’s how big equity is. Be wary of those who think they have all the answers and want to package it off as some kind of gift, layered with academia language. It’s like we are all back in teacher’s college, treating education like it is a science experiment — and completely forgetting it is filled with wonderfully imperfect humans.