Thursday, May 4, 2017

math instruction ready to retire

Retire: Key Words
I cringe when I see an anchor chart (no matter how cute) for mathematical key words in a classroom. First of all, there are many strategies in which to approach any word problem and to reduce kids to one because of a certain word can actually hinder their natural process. Also, it's straight up misleading. Take, for example, these two word problems.
A. Bob had 3 apples and Judy had 5. How many do they have altogether?
B. Maggie had 3 bags and each bag contained 5 apples. How many apples does she have altogether? Students who have been trained that altogether = addition are robbed of looking at this problem for what it is rather than simple words within. There are many instances where addition (adding up to) can be used to figure out "difference" problems (difference is often associated with subtraction).
Word problems are important (though not as important as we think) but the whole reason they exist is to get students to dig deep and really understand math in the real world.
Hire: Understanding/Explanation Of Problems
Instead of introducing key words, practice modeling what a problem is truly asking you. Have students dig to the root of any problem they come across before they start using any computation.
I like to have students explain to me what the problem wants from them in order to get a solution. No numbers, no computation, just truly telling me what answer (or kind of answer) they are looking for.
Don't believe me? Just read this quote from
teach a student to problem solve

Retire: Double Digit Addition/Subtraction Algorithm (traditional)
I will let you know this is my number one pet peeve (yes, even higher than the key word anchor charts - at least they're cute.) There is no, absolutely no reason you should be teaching students (especially young students) the traditional algorithm for double digit addition and subtraction. Yikes! Let's look closely at some reasons why.
  • It robs them of important place value understanding (which will only confuse them later - ahem, regrouping)
  • They can and will forget it and have no understanding to fall back on so they can figure out a problem.
  • It is not the strategy that comes naturally to everyone - heck, it's probably not the way you add bigger numbers in your head.
  • There are so many better ways. SO MANY.
Hire: All the other ways that actually lend to understanding and retain place value
The number one question I get on this blog or from my Instagram is how I have kindergarteners doing double digit addition (with understanding!).
Here it is, people.
I did not teach it to them. They have a great number sense, a fantastic understanding of place value (a top priority to me B.O.Y.) and they understand it. We never ever did a lesson on it. They saw the problems on a test (not created by me) and we had a discussion about strategies they could use to figure those out and they ran with them. They all figure it out differently.
Teach your kids to count by tens from any number and they will have a pretty solid way to figure out double digit addition (with or without "regrouping").
  • Hundred chart - your kids should be SO FAMILIAR with this it's like seeing their name
  • Open number line - don't underestimate - a LOT of kids understand math this way - this is the way I do math in my head and when I finally learned about open number lines, my mind was blown. My students do open number line problems at recess.
  • Stretch the numbers out (place value addition) - always retain place value - MUST
  • Count on (mental open number line)
  • Build the numbers and put together (concrete)
Retire: Timed Fluency Practice (any computation)
Computation is one of the least important parts of a real mathematician's job (hello 2017 and constant calculators!) and yet is the number one aspect pushed in elementary math. I'm not saying fact fluency isn't at all important, but it simply isn't as important as understanding. Students need to be able to do so much more than spit out facts. They need to reason, understand what a problem is asking of them, solve creatively, accurately, and efficiently. Do you see how all of these things are not accomplished with a sheet of isolated problems?
Furthermore, the speed with which a student can regurgitate facts is simply not important. I would much rather my students have multiple strategies to solve a computational problem than be able to memorize them. As long as students have understanding, the fluency/memorization will come.
Timed tests do nothing to help us assess our students' understanding and they certainly don't help students with their understanding.
Also, timed tests are a very high stakes activity and competitive in nature. This perpetuates a negative stereotype of math - prompting kids to believe that if they aren't fast, they aren't good. Again, this is not true.
Hire: Fewer problems that promote understanding
Instead of a whole sheet of problems, give students a word problem, logic puzzle, or challenge that involves the computation you are covering. You only need a few problems to assess student understanding and will also not stress students out. Also, cut out the time component altogether. Let's think about the message we are sending to our kids.
Some great ideas for activities that get kids computing without pressure are

  • Math magic (those pick a number, add 5, double it, subtract 2, blah, blah that are all over the internet. Kids think they're fascinating and they will work hard on computing to find a number that might not work)
  • Open-ended tasks (my favorite is to give an empty equation with a number answer for students to complete)
The challenge is for students to find multiple ways to complete the equation. I had a student give up "manipulative play time" to figure his out in more ways.