116_Why Teaching Math Is So Hard

Why Teaching Math Is So Hard Dan Kennedy Baylor School Teaching math is so hard because… Mathematics is not something you learn Mathematics is something you This makes mathematics different from virtually every other subject in the traditional school curriculum Here are some things that some people can do: Juggle Waterski Play the violin Dunk a basketball Run a marathon Mathematics Other people cannot People never say, “I never could English,” or “I never could History.” These are subjects you learn People not readily excuse themselves for not learning And who defines what it means to “do math?” Math teachers This is a big difference between the ability to mathematics and the ability to read! Someone who can read this sentence knows how to read How about this sentence: Ontogeny recapitulates phylogeny What does it mean to mathematics? + = 24 ÷ = Solve for x : ( x + 2)(2 x − 3) = 49 Find cos(π / 3) Find the product: 874539 × 374958 Find 239121 What is eπ i ? Do we teach students to mathematics or to understand mathematics? 1 −1 – – – −1 2 1 −1 + + + + + – (–4) – (–4) – = 11 Compare this to: So how we justify teaching a meaningless computational trick that is ONLY good for computing 3-by-3 determinants? It does not generalize to higher orders It does not even suggest anything important about how determinants work! Teaching math is so hard because… The people who must identify which students cannot mathematics are the same people entrusted with teaching them Their math teachers! The former paradigm: Learn the mathematics in a context-free setting, then apply it to a section of “word problems” at the end of the chapter I can the math… I just can’t the stupid WORD PROBLEMS! Graphing calculators have made word problems more accessible to students The emphasis has shifted much more toward modeling An example of a problem that used to be hard for students but that now is easy: 5h + f + 5d = 19.40 3h + f + 2d = 11.05 6h + f + 3d = 21.25 After modeling the problem, there are two easy methods of solving it: For teachers, these changes have not come easily We have made changes, hopefully for the better You might think we could pause, reflect, and enjoy what we have accomplished But that is not how technology works! Here are a few changes we have yet to make… We need to stop thinking of a student’s mathematics education as a linear progression of skills that must be mastered Arithmetic Fractions Factoring Equations Inequalities Radicals Geometry Trigonometry Calculus Statistics Proofs Functions If students who have not mastered our traditional mathematics skills can solve problems with technology, should it be our role as mathematics teachers to prevent them, or even discourage them, from doing so? Dr Retro, I’ve got it! That does not count, Miss Nouveau Put that thing away We ALL must teach fundamental mathemics skills to our students, who probably will not have mastered them Patiently Casually As a matter of course Mr Oiler, if there are twice as many dogs as cats, doesn’t that mean that 2d = c? Mr Jones, if that is all you learned last year, you had better drop this course before it drops you Good question, Mr Jones Let’s see what would happen if there were cats… We must honestly confront the goals of our current mathematics curricula Just because it is good mathematics does not mean that we have to keep teaching it Nor is it necessary, advisable, or perhaps even possible to teach everything that is in your textbook We should treat every mathematics course as a history course – at least in part We will probably always teach some topics for their historical value MATHEMATICS Technology Culture Mental Discipline Quantitative Literacy Research (College Prep) But whatever you do, have fun! Learning is enjoyable So is teaching Any other philosophy of teaching and learning is counterproductive Even in mathematics! dkennedy@baylorschool.org .. .Teaching math is so hard because… Mathematics is not something you learn Mathematics is something you This makes mathematics different from virtually every... “do math -because they could not “do” some things that we no longer even teach today! For example, here is what we were doing 45 years ago: Teaching mathematics is so hard because: This is America... determinants work! Teaching math is so hard because… The people who must identify which students cannot mathematics are the same people entrusted with teaching them Their math teachers! A sobering thought: