Real Math Teaching and Good Testing Works for All Students

This is a guest post by Ted Nutting.

I’m a retired Seattle mathematics teacher.  I’m alarmed by the proposals to address racial bias in our schools by doubling down on “inquiry-based learning” and by doing away with standardized tests.  These proposals are offered in the name of the Black Lives Matter movement, but hard-won experience in our schools shows they don’t help Black students.  The method harms students of all races. 

“Inquiry-based” or “discovery” math is not new.  Schools have been using the “wander our way to the answer” method of teaching mathematics for 25 years.  It has students working in groups on projects that aim to discover abstract principles.  (This is the “discovery” part.) It has students writing in journals to describe how they would solve a problem.  It has students using calculators instead of pencil and paper.  It is reluctant to test them to see what they know.

Teachers learn this approach in college. They are told the teacher should be a “guide on the side” rather than a “sage on the stage.”  As a way to learn the world of numbers it is too much about words.  The wandering to find the answer wastes students’ time.  The group projects allow less assertive students to fall behind, and not testing allows the teacher not to notice.  The whole approach is the main reason why our country is behind so many others in the math competence of our students. 

Now it is claimed that we need to teach this way in order to help Black students, as if they learned differently from others.   Baloney!  Here in the Seattle area we have lots of evidence in high-minority schools that real math teaching, in which the teacher actually teaches, gives far better results.  Mercer, Denny, and Aki Kurose Middle Schools in Seattle have fared very well on state math tests after being taught this way.  A 2017 Seattle School District study, “Middle Schools that Narrow the Opportunity Gap in Math,” confirmed this.  The Seattle Times featured two successful high-minority public schools:  Gildo Rey Elementary in Auburn in 2014 ( and Foster High in Tukwila in 2016 (  Both made huge improvements teaching real math. 

For the last seven years of my career, my students at Ballard High School (not a gifted magnet school) achieved far higher results than those from any other Seattle district school on the AP Calculus test.  In the one year that I taught a course for which there was a state end-of-course test (Algebra 1 in the 2011-2012 school year), my students scored better than those from any other teacher in the district.  I have the data to prove all this. Why did this happen?  I broke the rules and taught real math.  In calculus, I used a textbook more aligned with real teaching than the book I was supposed to be using.  In algebra, not having an alternative textbook, I made up my own worksheets to accompany the lessons I gave.  I actually taught.  I presented the material, asking questions frequently to keep students’ attention, and I gave difficult quizzes and tests.  I demanded good performance — and the results were excellent. 

Yes, let’s help Black students learn mathematics.  But results won’t improve if we keep doing things that don’t work.  Let’s not destroy our few recent gains and continue to inflict on them the “inquiry-based” method that has been such a disaster for an entire generation. 

And let’s not drop standardized tests.  A good standardized test (and the AP Calculus test is one) shows how students are progressing in respect to some standard.  If we don’t use such a test, how shall we assess students’ progress?  Scrapping the tests will only hide problems.  Classroom grades are not a substitute.  For many years I saw students move on each year with little understanding of the material.  Their grades were O.K., but their teachers had graded them too easily.  The result has been astonishing percentages of students having to take remedial math in college.  Good standardized tests can identify the students that need our help, and indicate what help they need. 

Let’s not allow current demands for change to lead us down a road we know will be harmful. Our schools should teach real math. 

Ted Nutting taught mathematics at Ballard High School from 1997 to 2014. He lives in Seattle.

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4 Responses to Real Math Teaching and Good Testing Works for All Students

  1. David Flinn says:

    Great article James, thanks for sending. Dave

  2. Pingback: A “must read” by a former math teacher | traditional math

  3. MM says:

    There is no such thing as a good standardized test in 2020. It’s time to to render the Smarter Balanced Assessment to the dust bin. That would be a good start, and it’s time to break the College Board monopoly and make David Coleman quiver in his boots. Agree with your real teaching methods and assume it was not Common Core influenced.

  4. Kathy says:

    Right on!

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