Bring up timed tests for math facts at a dinner party or on a soccer sideline and you're likely to start a debate. There are those who feel that timed tests put the focus on rote learning which is obsolete in this day and age in which we can rely on calculators and computers for these calculations. Others laud the timed tests as they are seen as taking us back to the basics in a good way.
Last year, my own third grade daughter was time tested each week. On Fridays, she was given a table of ten facts to complete within 20 seconds. She "passed" by completing the test correctly on time for two weeks in a row. Then, she would move on to a new set of facts. As I lamented in my "Coverage vs. Mastery" blog post, I feel that this practice emphasized speed over depth for her. She memorized to pass, but I was not impressed by the depth of her understanding (granted, I'm a hard case). The timed tests had a much more demoralizing effect on a friend's son who would make himself physically ill on Thursday nights anticipating these tests the next morning.
When I asked about the reason for these timed tests, Mahesh Sharma was cited as the key influence behind the practice. Having spent considerable time working with Mahesh over the years, I found this particularly interesting.
The term "automaticity" has been coined to mean the highest rate of fluency: immediate, unconscious recall and understanding of a math fact. According to Mahesh Sharma, it means that a student can give a math fact within two seconds orally (three seconds written) without "counting concrete materials, tally marks, or numbers on a number line." I can see how this message has been interpreted to mean "timed tests are good." However, Mahesh also points out that:
The real value of learning basic mathematics skills today is not that one will need to use those skills per se; chances are one won't. Rather, the benefit is to make the abstract objects of mathematics and operations to them become so familiar—and seem so real—that one can reason about them using the same mental capacities one uses to reason about everyday things.
To accomplish this, Mahesh emphasizes building automaticity through conceptual strategies. So, rather than be satisfied with my daughter having memorized her "n times 7" table, I asked her how she knew that 7 times 8 was 56. I asked her prove it to me multiple ways using both a linear model and the area of a rectangle model with Cuisenaire rods. I asked her make a conjecture for how she could use the distributive property to decompose and recompose multiplication problems. That's the real point in gaining automaticity. That's number sense. Rote memorization is like having a taxi drop you off at the finish line of a race. It robs you of an experience that would strengthen you.
Stanford researcher and math education professor, Jo Boaler goes so far as to denounce and call for an end to timed tests in her essay "Fluency Without Fear." She cites studies demonstrating that timed tests are a major cause for math anxiety which has a crippling effect on math learners. She agrees with Mahesh that number sense should be used to gain fluency, and suggests an instructional practice called "Number Talks" to build number sense which leads to fact fluency. Here is a video that demonstrates the idea:
In my own classroom, I had my students focus on deepening their understanding of multiplication by focusing on decomposition and recomposition strategies using the distributive property. We used the Cuisenaire rods to build the concept. When students felt ready they would time themselves using a stopwatch (sometimes they would work with a partner if they wanted to) and tracking their "personal bests" themselves in their math notebooks. This worked well for us, but I know that there are other creative ideas out there.
So, there is a role for automaticity, but automaticity and timed tests are not synonymous. However, we do need something that is organized and systematic that focuses on building number sense. In our 2013-2014 WCSU Comprehensive Math Review, the reviewers noted this need. In the absence of those timed tests (dreaded by many) that emphasize rote memorization over conceptual understanding, how would you promote automaticity?
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