After reading Dr. Boaler’s post on timed tests and math anxiety http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/, I can’t help but think about the amount of harm we are causing.
To automatize? Or to memorize? That is the question! But should there even be a question as to which one promotes student understanding? The debate between automaticity and memorization is very disturbing to me and the Common Core’s repeated use of the term “fluency” has only added more fuel to the fire. There is a massive misconception among educators that fluency means fast. The term fluency has been thrown around the English/Language Arts portion of the curriculum for years and I think it is for that reason that many teachers take the term fluency to mean quickly. Webster’s dictionary defines fluency from the word fluent which means “to speak a language easily and very well.” Nowhere in the definition does it mention speed or a time to completion ratio. Third grade students are required to read 110 words per minute by the end of the year. In the past I have had students read 80 words per minute but have 100% comprehension. Does that mean the student is not efficient at reading? I would hope not. Speed and the rate at which a student is able to complete a task in both reading and math will increase over time through continued purposeful practice. In the same breath, I have had students that can read 150 words per minute they are not able to recall a single word they just read. What’s wrong with that picture?
What time could one consider a student to be fluent? Three seconds, five or more seconds? There is no way to place a time on fact fluency and call it efficient. What can be done is to make sure the students knows and shares the strategy they are using. The art of sharing is something I believe to be one of the major missing components within today’s classrooms. In terms of math, not only is the practice portion of increasing fluency important, just as important is a student’s ability to share strategies and reasoning to cement understanding.
Teachers assume that because a student is able to recall a fact they must have it memorized, when in fact this couldn’t be further from the truth. Many students are able to recall facts through the automated use of a strategy. I have encountered teachers, including myself, that have promoted timed tests (those were the dark years of my teaching). After about three weeks of daily multiplication drills, 75% of the class has moved on to larger facts but 25% still remained at the multiplication facts for 0 and 1. But without reason, I’d continue to wash, rinse, lather, and repeat as struggling students showed no “improvement”. All students were told to do is keep working on their facts and get them memorized. There was no remediation taking place to assist my struggling students. I cringe when I think about the negative impact this might have had on each one of my students and I want to personally apologize to each and every one of you. Please consider this my formal apology. We as educators need to stop and reflect on the negative impact we are having on our students by cramming facts down their throats.
I keep thinking of a conference I attended with the workshop entitled 10 days to Multiplication Mastery. As I saw the title I couldn’t help but think about how many students are going to learn their facts and have no clue what they are doing. Better yet… how many teachers will attend this workshop and think it is the greatest thing in the world and push it on all their kids because “They gotta know their facts!” A teacher said the same thing to me this year as we were having a discussion. I agreed with her to a point that it helps when students know their facts. However, in addition I replied that the ability to recall facts does not completely limit students as to what they can think and do mathematically. John Van de Walle says it best when he states that “students who have total command of basic math facts do not necessarily reason better than those who, for whatever reason, have not mastered math facts.”
As a math coach, this is a battle I encounter each year. I’ve explained my issues with timed tests and their negative impact but many teachers refer to this approach to fact fluency as “new math”. I’ve tried to explain that there is no “new” or “old” math …just research that supports a constructivist’s approach to student learning and that research show tremendous student growth over time. After all, is improving students’ achievement why we as educators are in this profession?
I (politely) but strongly disagree! Math is a beautiful combination of both reason and automaticity. If you have one without the other you will not be successful at this age. Later on in life, when you are able to use a calculator you can survive of merely reason.
Thanks for the comment Brittany but I think we agree…or at least I do with you:-)
I completely agree with everything you said. Automaticity CAN’T be built without reasoning but reasoning CAN be built without automaticity. Memorization of facts requires no reasoning.
An example: a student that is able to invent their own strategy must be grounded in solid reasoning. If a student can reason they will be successful because, as you mentioned, the calculator will take care of the speed issue in the future. Automaticity is built through the repeated reasoning and use of a particular strategy. The repeated use of the strategy enables the student to become so fluent in recalling their strategy, that it appears to be memorization when in fact it’s not even close.
I think the point I was trying to make was that if a student has automaticity it is built through strategy and reasoning, whereas memorization is nothing in and of itself….but the memorized fact
The CCSS state that students should learn their facts “from memory” which is automaticity…not memorization. Although I wrote this over a year ago, I hope I painted a clearer picture of what I was trying to say a couple of weeks ago. https://gfletchy.com/2014/12/01/from-memory-and-memorization-there-is-a-difference/
Thanks again for your comment and helping me paint a clearer picture. I appreciated it. Cheers!
This is so true! Many of us as educators have been guilty of doing this, and I too feel guilty about the meaningless pressure and stress I placed on my students. But rather than memorize their math facts, lets focus on understanding their math facts, possibly focusing on creating models, manipulating the numbers and verbalizing.