Two months ago, Jordyn Marie was born. Nothing can match the joy of having a child, unless it is the birth of a grandchild. If you ask me, she is pretty darn perfect, and as a devoted Nee’Nee’ (my name for grandma) I would like to keep her that way. I would like to make her life, most especially her school career, as smooth as possible. Therefore, I have compiled a list for the future math teachers who will be tasked with ensuring Jordyn’s math understanding. Here are the top 10 things that her teachers need to make sure they are doing by 2018:
1. Problem Solving, Problem Solving, Problem Solving!!!-Children need to be daily problem solvers! Their ability to do just that will be measured in our assessment system and is an essential life skill. As a math consultant I believe nearly every math concept can be taught through problem solving with some “just-in-time” direct instruction. Teachers need to be trained to facilitate learning through constructivist methods, schema based instruction (such as CGI), or inquiry based instruction (Dan Meyer model). If Jordyn is to be prepared to live and work in the world beyond her formal education, she will need to be able to solve problems and apply mathematics.
2. Insist on precision. Not only should Jordyn be required to supply the correct answer to problems, but she should also be required to know what the number represents. Of course this requires problem solving, problem solving, problem solving. (see above) No one knows what “37” represents in a “naked number” probem but we do know it represents “37 cookies” when it is framed in the context of someone eating 13 of the 50 cookies in a package. Another area where precision is required in mathematics is in its vocabulary. Teachers and students alike need to know the precise meaning of mathematical terms and use them correctly. Don’t baby her along. I know she is a little kid, but little kids love big words, and when taught in context even little kids can learn them.
3. Multiple Strategies and Representations (CRA): Do you know there are 28 ways to teach subtraction and the USA is the only country that has taught only 1 of those methods? I want “Jordyn’s Method” of representing a problem to be acceptable in your classroom. As she solves problems in your classroom you should be questioning her as to how she arrived at her solution, not dictating the method. She should also have the opportunity to represent her solution with a Concrete tool, a pictorial Representation or with an Abstract algorithm if it makes sense to her and she can explain her thinking.
4. Tools, Tools, Tools! Unifix cubes, color tiles, base-ten blocks, pattern blocks, number lines, clocks, 100’s and 200’s charts, tens frames, double tens frames, dice, dominoes, playing cards, play money, counters of any kind (beans, buttons, chips, etc…), two-colored counters, hands-on equations, measuring devices, calculators, etc….she should have access to all of these and have the right to choose the ones she wants to use to solve problems. Your classroom may be a little messier than it used to be.
5. Critical Thinking/Argumentation/Cooperative Learning: These three are all life skills and they all go together. Kids need to be critical thinkers. They need to hear thinking modeled aloud and they need to have opportunities to practice this in a safe environment. They need to learn to communicate their thoughts to others in the same way. Kids have to be allowed to work and talk together about mathematics. Your classroom may be a little noiser than it used to be.
6. Differentiate: Not all children are ready for the same problem type at the same time. Listen to your students, notice the ones that finish quickly and do have true understanding of their answers. Some take longer to solve and need more questioning to help them reach true understanding. Know which type of child Jordyn is. If she needs time, let her take it. If she needs to be pushed, extend her with a more difficult problem.
7. Create an environment where students “Embrace the Struggle”-don’t enable her! I know you went into teaching because you love students and you never want to see them struggle or fail but the definition of “problem” is that it is something that cannot be solved immediately. Teach your students that fast isn’t always best and that being incorrect isn’t a failure; it is merely another opportunity to try. Teach her to persevere.
8. Throw away the worksheets and most of the timed tests: There are so many instructional strategies that will allow you to assess what Jordyn knows and give her repeated practice on skills other than worksheets. Save a tree and quit using worksheets and workbook pages. Save another tree and keep timed tests to a minimum. Math facts are important but timed math facts tests should only be used as a formative assessment so see which facts kids know and to drive your instruction on the ones they don’t. Use them sparingly and help lessen the math anxiety in children.
9. Help her generalize but not overgeneralize: I want Jordyn to discover the properties of math (zero, identity, commutative, associative, distributive, etc…) but I don’t want her to develop misconceptions that can be avoided. Too many repititions of problems like 4 + 3 = ___ could lead Jordyn to misconstue the meaning of the equal sign. I don’t want her to believe the equal sign means “put an answer here”. I want her to discover early on that the two sides of an equation must be balanced. Problems like __ = 4 + 3 and 8 + 4 = ____ + 5 will help with that. I don’t want her to believe that all plane shapes are regular. Help her classify triangles that aren’t equilateral, octagons that aren’t shaped like stop signs and pentagons that don’t look like a building in Washington D.C.
10. Make it FUN; help her LOVE Math; and always remember: Nee’Nee’ will be watching!