We Need to Stop Giving Timed Tests in Math – What Shall We Do Instead?
We highly recommend this ASCD audio interview with Jennifer Bay-Williams, one of the authors of “Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention”. (If the book is too pricey, here‘s a companion website with some of the resources.) Her main points coincide closely with our own experience. Here are our thoughts:
1. Why stop giving timed tests?
- Timed tests do not teach math facts. We do not see increased acquisition of facts happening during these quizzes. They only serve to sort students by speed. How sad is that?
- In fact, these tests interrupt learning, substituting assessment time for more productive learning time. Almost as sad, right?
- Timed tests fail as an assessment tool, giving us very little insight into how a student is approaching their learning. Are they counting on? Guessing? Skip counting? Doubling? Other than recall speed, the tests tell us very little.
- We encourage teachers to give students the time they need to learn their math facts by developing their own strategies. The big advantage is that such strategies are transferable. If I know from my 20-frame at right that 9 + 6 is the same as 10 + 5 (by moving one marker to make 10), then I will know later that 11 twelfths plus 6 twelfths is one and 5 twelfths, and that 9 tenths (0.9) and 6 tenths is 1 and 5 tenths (which visually is easily recognizable as 1 1/2) , and that 9 groups of 3 plus 6 groups of 3 is 15 groups of 3, and therefore 9(x+4) + 6(x+4) = 15(x+4).
Yes, this takes more time, but (a) in our experience, the students do get to fluency, and (b) everyone gets there, not just the select few who find memorization easy. For an impassioned condemnation of memorization, watch this video from (the normally mild-mannered!) Yeap Ban Har, leading architect of Singapore Math.
2. What to do INSTEAD??
- Use visual learning. For. A. Long. Time. Twice as long (at least) as you think is necessary!
To see how perplexing yet amazing it feels to learn this way, try this wordless, animated proof of the Pythagorean Theorem by Bhaskara of ancient India. (Just drag the little bead in the top left of the screen, then spend a while thinking about how he started with a square on the hypotenuse of each colored triangle.) According to legend, all Bhaskara had to say when he presented this theorem was “Behold!”
Examples of using visuals in elementary math here (from Jo Boaler), research data here, our own blog’s examples here and a whole video series here (the inimitable James Tanton with Great Courses).
- Withhold the algorithm. “Ask, Don’t Tell” — let them figure math out, with guidance in the form of questions, feedback on their insights and “I wonder what would happen if we….” prompts. This is not a new fad idea. From the 1970s on, John Van de Walle of Virginia Commonwealth University was amassing a huge following of dedicated teachers with his books “Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades K-3 (and 3-5 and 5-8). These books give a us a full curriculum sequence of visually-based learning; he shows how to guide students to develop strong conceptual understanding without all the algorithmic drill. He was a man ahead of his time.
- Games. From the above-mentioned interview with J. Bay-Williams: “Games are an excellent vehicle for learning and practicing strategies. When students are playing games, they’re having fun, they have no stress, which means they can really focus on what they’re trying to do – use strategies. They have a partner, so they talk to each other – ‘Thinking aloud’ is one of the best learning strategies, especially for students who struggle. And they’re hearing their friend’s strategy.” So they’re learning to see math as a living, approachable, sense-based system. As Yeap Ban Har says, focusing on number strategies confers students with a flexibility of thinking. We’re turning them into little mental math gymnasts!
There’s a caveat to playing games, though — the games should be strategy-heavy thinking games, NOT speed-based competitive games. (Perish the thought!) The Math For Love website has a good collection of games, as does Denise Gaskins of “Let’s Play Math”. And Michael Minas at LoveMaths. Oh, and Thinking Mathematically, and Living Math and Wild Maths.
- Number Talks. Here’s a long list of resources for number talks (From San Francisco Unified). For upper elementary, we also love the FractionTalks website.
- Everything else. ALL math work builds math fact knowledge. It’s the difference between math practice and math drill. Practice means using your math facts every day – and practice will get you there (so much less painfully) in the end. So word problems, puzzles, investigations, 3-acts… why shouldn’t math be fun?
- Finally, assessment. The best assessment is observational. The Kentucky Center for Mathematics shares lists of tools to use when interviewing or observing children’s progress. We watch for these major occurrences:
If a child still needs concrete materials, FINE! You can’t rush this. You can’t force neurons to connect. But watch for this: are they gradually moving more than one block at a time? Exchanging more efficiently? Predicting borrowing? Seeing tens/ hundreds? Rejoice – they’re about to move on.
Pictorial: Yay! Students can represent their own thinking on paper, 2-dimensionally. A huge step. What to watch for: are they developing their own shortcuts? Crossing out part of a drawing rather than borrowing? Stopping half-way through and telling you the answer because they’re able to see it coming? Again – feel the joy.
Abstract: Yay again! This is what math truly IS. The abstract representation of reality. Why learn math? Because math is actually less complex than reality. It’s not until we fully understand the concept behind a math procedure that we see it for its efficiency and simplicity. What to watch for? A student sees someone use the algorithm, and says “Hmmm… that’s what I’ve been doing, but it’s more efficient. I like it.” Voila!