How long should a timed multiplication test be

Timed tests convey a message that success in math is about " performance ," which is very misleading. However, that is not really true! I find it very interesting that mathematicians can be SLOW. The reason is — they're thinking deeply!

Please read the following quote from one of France's greatest mathematicians, Lauren Schwartz, who won The Field Medal in math. She reflects on being slow in school: "I was always deeply uncertain about my own intellectual capacity.

I thought I was unintelligent. And it's true that I was, and I still am, rather slow. I need time to seize things, because I always need to understand them fully. Even when I was the first to answer the teacher's questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who read as good as I was answered before me, and towards the end of the 11th grade I secretly thought of myself as stupid and I worried about this for a long time.

I never talked about this to anyone but I always felt convinced that my imposture would someday be revealed. The whole world and myself would see that what looked like intelligence was really just an illusion. Now that never happened. Apparently no one ever noticed it, and I'm still just as slow. At the end of the eleventh grade, I took the measure of the situation and came to the conclusion that rapidity doesn't have a precise relationship to intelligence. What is important is to deeply understand things and their relations to each other.

This is where intelligence lies. The fact of being quick or slow isn't really relevant. Naturally, it's helpful to be quick, like it is to have a good memory. But it's neither necessary nor sufficient for intellectual success. How can we teach math facts then? I have gotten lots of positive feedback about them from others as well: Strategies for addition and subtraction facts Learning the multiplication table of 3 with a structured method To develop number sense beyond the basic facts, you can use so-called number talks — short discussions among a teacher and students about how to solve a particular mental math problem.

Further reading Value of mistakes in learning What are number talks? Expectations of automaticity vary somewhat. Translating a one-second-response time directly into writing answers for one minute would produce 60 answers per minute. However, some children, especially in the primary grades, cannot write that quickly. Howell and Nolet recommend an expectation of 40 correct facts per minute, with a modification for students who write at less than digits per minute.

If measured individually, a response delay of about 1 second would be automatic. In writing 40 seems to be the minimum, up to about 60 per minute for students who can write that quickly. Teachers themselves range from 40 to 80 problems per minute. Sadly, many school districts have expectations as low as 50 problems in 3 minutes or problems in five minutes.

These translate to rates of 16 to 20 problems per minute. At this rate answers can be counted on fingers. Ashcraft, M. The development of mental arithmetic: A chronometric approach. Developmental Review , 2, The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1 — 6.

Journal for Research in Mathematics Education , 25 5 , The production and verification tasks in mental addition: An empirical comparison. Developmental Review , 4, Is it farfetched that some of us remember our arithmetic facts?

Journal for Research in Mathematics Education , 16 2 , Campbell, J. Network interference and mental multiplication. The role of associative interference in learning and retrieving arithmetic facts. Rogers Eds. Cognitive process in mathematics: Keele cognition seminars, Vol. MissCeliaB , Aug 18, Obadiah , MrsC and Leaborb like this.

Joined: Sep 16, Messages: 6, Likes Received: 2, Aug 18, Timed tests, just like flashcards, are designed for fluency of facts students already know. They are one of the most misused practices. For kids who struggle, give them all the time they need. I would include a lot of accurate repetition in class. Have those kids who know their facts cold move on to something else, but those who don't work on recitation and accurate production using multiplication tables.

Joined: Sep 30, Messages: 24, Likes Received: 2, Aug 18, I give them as much time as they need on a problem 'assessment' Students know they can set goals regarding increasing the number correct or working on fluency speed. I use it more to notify parents than for a 'grade'.

And I only give it one after we've spent a lot of time on all the 'facts'. Aug 18, Leaborb, that is horrible. Leaborb likes this. Aug 19, This article showed up in my Twitter feed this morning--some interesting thoughts. MrsC , Aug 19, Joined: Nov 20, Messages: 2, Likes Received: 1, Aug 19, It's funny: as someone who got a math degree, K math ed cert, as well as what I'm using mostly right now - my K-8, you'd think I'd fall exactly along with the comments so far That being said, I currently - though it really began because my other colleagues were doing so as well in my first two years - do a quick math facts assessment at the beginning of each month.

In talking with parents, my discussion is all around how it isn't the end-all kind of assessment, but that facts being readily available is important for freeing up the mind to work on the other concepts and reduce computational mistakes.

The last fourth of the class tends to be the ones I work with a bit more - and we'll focus on strategies such as 8x9 - doing 8x10 and subtracting 8 or doing 8x8 and adding 8 or 4x I have a vast variety of materials for them to practice with: worksheets focusing on one fact, worksheets focusing on mixtures of facts I tell them to avoid this unless they're just needing to work on accessing it quicker, and really then, it usually comes without much practice , playing cards, white-erase booklet that has one set of facts x1, x2, etc In the end, there's not a ton of focus on it, and I haven't found or seen much of any negative feedback from the kids, especially since it's just a once-a-month kind of thing to see where we're at.

Separate of my team, I started utilizing it as an opportunity to work on growth mindset: students have a graph for multiplication and a graph for division facts, and they graph each month where they are at, as well as reflect on what practice might help them struggling with x5s? Know them all but it just takes a while?

Similarly, as a class, we have two bigger graphs where we track the average for the class - discussion again is all around trying to make it grow, and there's no pointing out of individual students within it.

I'm in the process of reading a book by Jo Boaler, one of my favorite people in education, and I'm sure that will change my thinking a bit - but I feel like I've found a relatively happy medium for the time being.

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