# “What’s 6 x 8?” and Calculator Dependency

Since getting back into the classroom, I’ve been reminded how much students struggle with simple mental math. I cannot even begin to account the number of times I hear “What’s 4 x 7?” or “What’s 4+19” blurted out in math class. When I follow up these questions with “You know this, take a second and think about it”, I sometimes am told that they just can’t and they grab their calculator and punch it in before I can get anywhere.

I have been thinking a lot about how I can combat this daily struggle. As much as I’d like to, I don’t think I can afford to take a few days away from my plans to reinforce a deeper understanding of arithmetic. In a perfect world, I could take a week and use manipulatives and applets and anything else of value to really develop a deeper understanding in my students. I’m not sure it would be acceptable if my students fell behind the other sections to review “elementary” skills. Then again, as I write this, maybe it wouldn’t be so bad if my students got something out of it.

As I start to think more and more about this, I even start to wonder if it’s really a big deal. Almost every one of my students has a phone with a calculator on it that they can whip out and use at any point in their daily life. Those that don’t, probably can find access to something that does the same trick very quickly. If they’re going to use calculators outside of class when they try to use math in the real world, should I be wasting my class time trying to reinforce skills they won’t need or use.

I do have an idea. I don’t think it’s perfect, but I hope to refine and develop it in the conversations that follow this post.

I am considering bringing “Mad Minutes” into my high school math classes. I’m not sure if that’s what they are commonly called, but that’s what they were called when I was a student. Basically, students get a sheet with 40-50 simple addition, subtraction, multiplication, division, or whatever you’d like. Then you start the timer and they try answer as many of them correctly in a minute. We would always get a score, which was the number of consecutive correct answers. I remember being successful with them as a young student. But I don’t know if they work for everyone or really work at all.

If I were to bring mad minutes into my classroom, I don’t think I could justify grading them. I would, however, want to keep a record of how everyone did and see if there is any progress made. But, most importantly, I would want to see if there was a reduced use of calculators or those “What’s 5 x 9” questions.

Is there something better out there being used to combat this in math classrooms?

Photo Credit: josef.stuefer via Compfight cc

I have thought about this before. I even bought a book once (lent it to someone…don’t think I ever got it back). I’ve never tried it. And I don’t have any answers.

But just to feel like I’m contributing something…

One little thing I tried differently this year in Algebra 2 was a ‘trick’ while factoring quadratics by grouping. I teach them to put the a*c on the top of a T chart and b off to the right. (some people use an X, but it doesn’t have enough room for what I have them do). I have them list factor pairs starting with 1 and the number, having them go in order least to greatest on the left so that when they’re close, they know they’re done. It helps to make sure they haven’t missed any, teaching them little tricks about different numbers along the way.

I’ve always tried to encourage them to use the ‘tricks’ I do like seeing if a number on the right can be cut in half, then I can double the number on the right. Look up at the numbers to see if you can see a particular factor in any of the numbers (this is hard to explain in words). But this year, in particular, it seemed like their number sense is even poorer than the past (some, of course, not all). So the new trick this year was to have them factor down to prime factors and then show how they can mix and match. This seemed to be a revelation to all I showed it to. I’m hoping they’ll think about numbers just a little differently/better.

PermalinkI think those extra tricks are important to bring into the classroom. What I’ve tried to do in the past is show or help one of my stronger students realize it. Once they see how much easier things can be with it, I try to get them to teach the rest of the class with the extra time they always seem to have. It’s worked wonders. The students take ownership of it and like to learn from each other a lot more than they do from me.

PermalinkI know that our 3rd grade teachers give timed tests. Many parents often want to know what purpose they serve. This is a good example of the purpose they serve. I am in Math for Elementary Teachers and we are not allowed to use calculators on test that require easy math skills. Maybe you could give timed tests for extra points.

PermalinkIn my high school classes, I want to try to stay away from the extra points as much as I can. I have found that the students that need the extra practice typically aren’t motivated by the extra points since they’re struggling already. And the stronger students who jump at the extra point opportunities, don’t need the extra help and are only doing it because it’s an easier way to keep their grade high than to really challenge themselves. Obviously, this doesn’t apply to every student, but I think there must be a better way to gain these skills.

PermalinkHi!

I actually do timed multiplication “activities” with my 6th graders at the beginning of the year. They’re exactly as you described – not graded, but I keep a record of who struggled and recommend extra basic practice for those kids. I also don’t allow calculators in class 90% of the time because of the age and that a big goal is reinforcing those fundamental skills. We do a lot of mental math practice and discuss different strategies as a class so they can learn new ways of approaching problems.

Good luck – you’re not alone in that frustration!

PermalinkThe question that pops into my head as I read your comment is: When does this mental math practice disappear for our students?

It seems to me like somewhere in middle school, the emphasis on the use of mental math just disappears. Is it when calculators get added to the school supply list?

By the time they get to high school, many students seem to have lost that mental math skill. Maybe they just don’t want to think anymore by the time they get to high school.

PermalinkI think that there are several questions to consider here.

!.

You say “

I don’t think I can afford to take a few days away from my plans to reinforce a deeper understanding of arithmetic.” I say if not now, when? If you “give up” a few days to reinforce arithmetic, will it save you time in the end? Will you be able to go further, if you intervene and shore up some of their prerequisite skills now? I always worry that we are adding on to what they don’t feel confident about because we press-on.2.

Do we equate speed with accuracy and skill? As a learner, I struggled under the pressure of timed tests. I could not freely demonstrate what I knew because I was concerned about the clock. I think Mad Minutes are fine as a drill to build automaticity. I’m not sure if Mad Minutes will deepen understanding. I agree with you that manipulative and aplets can help. The real question is how to differentiate to meet the needs of each learner.

3.

Should the score be “

the number of consecutive correct answers?” Should the score be the number of correct answer, period? What value is there in the number of consecutive correct answers? I encourage my learners to skip around, to answers the questions they know first, to start from points of success.Good luck! I think this is a great topic to grapple with for learning, confidence, and success.

PermalinkI feel that I can’t afford the extra time because I’m a first year teacher. If I fall behind the veteran teachers who are more focused on getting through the curriculum, I worry about the backlash. But, I think you’re right. If it’s best for the students, it should be just fine, right?

The emphasis on speed with accuracy is my biggest hesitation with this. It’s an extra stress on my students, when I really just want my students to be better learners.

I really like the idea of allowing learners to jump around. If I do ever decide to try to this out, I think that’s what I’ll do.

I want my students to be successful. Thanks for sharing your input, these are things I need to consider before I move forward!

PermalinkHi Kyle,

Keen observation. With google/Siri in their pocket, do students still need basic computational math skills?

Sure.

JPLGough raises a number of reflective questions for any math teacher. I believe my thinking is similarly aligned with theirs.

To be mathematically proficient students need to have ‘procedural fluency’. Skill in carrying out procedures like addition, multiplication, and so on. However, this is only 1 part of being proficient in math.

Accoding to “Adding it up: Helping children learn mathematics” (2001), there are at least 5 intertwined components of math proficiency:

• Conceptual understanding (comprehension of math relations)

• Procedural fluency

• Strategic competence (ability to represent and solve)

• Adaptive reasoning (reflection, justification, explanation)

• Productive disposition (math is useful and I am good at it)

When you are doing your ‘mad minute’, will the 40 to 50 questions be purposefully chosen or created at random?

If created randomly, then I agree assessing the results might not be meaningful.

However, if the ‘string of math problems’ (Cathy Fosnot) you give students are purposefully chosen so as to highlight a specific math strategy or concept, then maybe student engagement with the mad minute (or math string) can go beyond the ‘procedural’ but also impact the conceptual, strategic, adaptive, and productive…

How might this look like in your classroom?

Thanks for posing an interesting question, Kyle.

PermalinkI haven’t read that article, but I am going to look it up right away. Those five components were topics that we always discussed as I went through my Education degree the last four years. They are things I’m always considering when I try to come up with my plans. However, I’m not sure mad minutes really hit as many of those components as I’d like.

If I were to bring these mad minutes in, I had imagined them being random, addressing a basic operation with each one. For example, one would be on addition, then one on multiplication, etc. Then we’d track progress in each specific operation.

I’m not sure that would count as being purposefully chosen, since all that’s being chosen is an operation. I think you’d have to go a different route with this if you wanted to hit some of the other components. Mad minutes are extremely far from the adaptive reasoning you mentioned. As soon as I try to bring in justification and explanation, it’s going to take the same amount of time as it would to do something that would create deeper understanding, like the manipulatives or applets I mentioned in the post.

Thanks for pushing my thinking.

PermalinkIt drives me nuts that the curriculum has eliminated the memorization of times tables. We spent hours in school learning them so now I make my kids write them every night.

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