October 22, 2017 at 2:32 PM #39126Hilary B Martin@vwbeetlegirl
How important is it to memorize math facts in the lower elementary? How do you implement the memorization if the curriculum does not call for it?
October 25, 2017 at 8:47 PM #39464Carolyn Martin@carolynmartin
Is it important? As a teacher, I would say, yes, it is important. Math lessons are much less stressful for student (and teacher) if they have the facts memorized. They can work faster and should be more accurate. In real life, we use facts at times we may not have a calculator handy.
That being said, there will often be one or two students who find memorizing the facts difficult.
What can you do to aid memorization. Of course daily flash card practice is important. If a teacher or aide cannot supervise the practice at least have partners spend time drilling each other. I like to have my students say the answers in unison for the facts we are learning and then do individual or small group drills with facts they need practice with (the ones they sort of know but aren’t speedy with). There are various games you can play with flash cards.
Reciting a table together will help some students learn them. For addition and subtraction facts above ten I use the triplets to teach connected facts. The numbers 11, 9, 2 will make the facts 2+9=11, 9+2=11, 11-9=2, 11-2=9. We chant all the triplets that go with 11 (11, 9, 2; 11, 8, 3; 11, 7, 4; 11, 6, 5) and add others as we get to them. Usually if a student is having difficulty recalling a certain fact just saying the triplet (and leaving out the missing number) is enough to trigger the answer. It works really well for subtraction.
Learn to skip count by 3’s, 4’s, 5’s, etc. to aid multiplication and division memorization. When I was in school we learned our multiplication tables by writing the table ten times. We were then quizzed on it (under time pressure) and if we missed any we wrote the table ten more times and were quizzed again. This went on until we got 100% on the quiz. Once we got 100% we moved onto the next table. Usually this meant that the students who passed the quiz the first time were exempt from the quizzes on that table until the whole class was ready to move onto the next table.
Give fact practice papers every day and require a certain amount correct. For students in 2nd grade and above, have some system that they can check their own or each others.
October 26, 2017 at 9:45 AM #39468Crista@cris
Singing the facts to a familiar tune of a song can assist some students in memorizing the facts. Example: the 4s multiplication facts can be sung to the tune of “Old MacDonald Had a Farm” or the 7s to the tune of “Happy Birthday to You.”
October 28, 2017 at 7:51 PM #39580Peter Goertzen@petergoertzen
As a high school business math teacher, I think math fact memorization is vitally important. (In general, the longer I teach high school the more important I think the elementary grades are, and the more respect I have for good elementary teachers.) Even though we often use calculators in my class, students with a solid grasp of their math facts are able to do their work more quickly and easily, and have a better sense of how numbers work together.
I don’t really know anything about how to make memorization happen, but I do remember that when I was in third grade all the students who memorized a certain set of math facts got to go on a special trip. It was A VERY BIG DEAL, and I know it motivated me.
October 28, 2017 at 10:58 PM #39583Betty Yoder@bettyyoder
I think we all agree that memorizing the math facts is essential. Using some form of touch and move manipulatives (such as the Rekenreks Ruthanna demonstrated on her recent video) is necessary to ensure understanding of what is happening. Obviously repetition of the facts being memorized using methods such as flashcards and fact sheets is important, but each student’s own learning style dictates how the basic understanding most easily moves on into the “memory mode”. As such, I think it behooves us to use a variety of methods and for those students that don’t “get it” using the methods we have traditionally used, we need to spread our wings trying new ways. We tend to teach as we best learn ourselves, but how I would most easily learn is not the best path for all my students. If a student is struggling, I ought not to simply assume that doing more of the same is always the best way to ensure memorization.
I thought of this a couple weeks ago when we were moving into memorizing multiplication facts. I know how I have taught it with a reasonable measure of success in the past, but thinking of one of my students pushed me to wanting to try a new method — the typical procedures would likely not work best with this child. Remembering a homeschooling mother telling me how she taught her challenged student the multiplication facts, I decided to try this new twist — I typed in large font the group of facts to be learned (the multiplication squares in this case) onto individual blue colored construction paper and posted them on the front chalkboard. Then each day one or more found their way to a new spot in the classroom — the 3×3=9 fact ended up on the plant pot up on top of the bookcase, the 6×6 on the classroom clock, the 8×8 on the fire alarm light on the ceiling, etc. Each day they would eagerly look around to locate the new fact. (I tried to find unusual places). When doing their fact sheet or flashcards, they were welcome to find the answer on the posted card, but within only a couple days I noticed that no one looked any more, instead they thought of the fact’s location: “Oh its the one on the clock”, etc. Pretty painless. Now this week they will come down, one or more at a time in preparation for the next group of facts to go up. Different color, different locations.
This new approach is working well with this year’s group of students but it would not necessarily be as effective with every group. There really is no “one right way” to teach all students. If we can be flexible in our approach and seek to teach to those who are more challenged, the rest will come right along. And if our teaching can include some element of surprise or off the beaten path ideas, we can cash in on positive emotions aiding the whole process for as students rehearse the pleasure in their minds, they think about the facts and the end result is the path to memorization is more easily traveled.
November 25, 2017 at 12:14 PM #41299Jonas SauderModerator@jonas
In conversation with an active school board member at a teachers’ workshop on the west coast last week, I was again reminded of the peculiar differences some of us experience in learning sets of basic facts, such as multiplication tables. He never learned the multiplication tables, although his full time work is property investments. When I asked him how he’d find the value of 6×7, he described a rapid visual way he’d see three sets of 14’s and add their sum.
He described his thinking methods in general as not approaching things “head on” like is generally taught (we train ourselves to explain things clearly, logically, and connect them to the “known”), but rather he somehow comes around and “in the back door” to understand things.
Just another reminder that among the groups we teach, there will be those who cannot master standard spelling (a rather modern requirement tied to standard print) or cannot “master” the lists of math facts, especially if mastery means being able to recite sets of number families for addition and multiplication.
And we need to humbly remind ourselves that one can recite the facts without much comprehension–and conversely some can have a deep intimacy with number sense and yet fail to memorize sets of facts. Some are mystified by the whole project.
So we teach. The teacher is tasked with mediating between his student and the subject, praying to understand how his student’s heart, mind, will, emotions and peculiar mental faculties function. Then he works with “what is” in the moment to help his student learn that which he would not learn without a teacher.
To learn basic skills and facts, effective teachers will introduce their students experientially to a wide variety of methods, including tactile, visual, oral, aural, and kinesthetic. Students may resonate with one or more of these approaches and learn to use them. Teachers are students of their students, seeking to learn how they learn–perhaps by encouraging them to articulate or somehow demonstrate how they know what they do know.
August 16, 2019 at 1:14 PM #75724
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