Working Memory in Mathematics
We’ve known since the skill was first labeled that working memory is
important in mathematics. It is the ability to hold information in your mind
and work with it. There is also a consideration of how much you can hold in
your mind while you work with it. Calculations that aren’t automatic require
working memory. Think about adding double digit numbers in your head, and
what you’re experiencing is your working memory as you hold the solved
digit in your mind while you complete the addition process. Our goals for
skills like calculation is to develop “automaticity;” in other words, that they
become automatic so that we don’t use up working memory space with them.
Our goals for procedures is that they become “consolidated,” meaning that
portions of the procedures link so tightly that we don’t even need to think “and” as
we proceed to the next step.
In recent years, research by Mark Ashcraft and others has shown that anxiety decreases working
memory. This presents double trouble for students having difficulty in mathematics. It appears that
anxiety decreases how much can be held in mind, and as things slip out we make errors. Naturally this
can further increase anxiety and a mathematical nightmare begins.
So how do we deal with this?
1. Of course, work on decreasing anxiety. Try the websites mentioned in the Decreasing Test
Anxiety handout. Also try meditation, yoga, tai chi, other stress management techniques or
regular exercise as ways to improve focus and decrease overall stress.
2. Develop automaticity where you can. If you’re in college and have not been able to calculate
automatically since elementary school, then don’t stress about it; use a calculator consistently.
But there are many other places in math where automaticity is important. When first learned,
we take time to think through these, but they can become automatic. Here are a few examples:
Identifying terms in an equation
The difference between factors and multiples of a number
The difference in the rules for calculating with integers
Placing ordered pairs on a graph
Interpreting math vocabulary
As you learn these concepts, practice them even more than requested (and this can take weeks)
so that you can do them almost without thinking.
3. Be aware of consolidating steps in procedures, and work to increase them. For example, as I
watch students learn to isolate a variable, they learn that if they subtract an amount on one side,
they subtract the same amount on the other side. At first, this is a two step process, but with
practice it becomes one: subtracting the same amount from both sides. Eventually, the longer
process becomes basically one step: isolating the variable. But consolidation doesn’t always
happen, which is one reason for additional time on tests for some students. If you’re a verbal
learner, work on decreasing the number of words you need to use to guide yourself.
4. Improve your working memory. With numerous companies developing “brain fitness”
activities, we have some pretty good research indicating that working memory can improve
with training, and that the skill level maintains for about 3 months after training is stopped.
Activities need to change when consolidation or automaticity develop.
Activities to Improve Working Memory
Of course, the ideal activities would involve some math; however, this may cause significant
discomfort and may not be helpful if calculation is involved and that skill is impaired. Here are a
variety of activities, based in math, language, or spatial skills. Key to improving this skill is to
mentally pre-plan, and to inhibit trial-and-error, impulsive moves.
1. Non-computer
a. Sudoku (uses numbers, but not calculation)
b. The 24 Game (calculation)
c. Word Jumbles (language)
Word Ladders and Word Morphs are also good.
d. Tangrams (visual)
e. Cube Nets (spatial) Mentally work these using the print-out from
(http://www.numeracycd.com/contents/activities/nets/netscube+puzzle.pdf)
f. Certain types of Solitaire, e.g. Grand Duchess, Spider (upper levels), Free Cell
The only problem with solitaire is that you simply lose; your errors aren’t noted.
Mentally plan how to uncover a card and then remember the steps.
g. Activities like mentally alphabetizing the letters in a word, played with another person
who checks your answer (and maybe takes turns so you have to do some checking)
2. Software Available in the HTC
a. What’s My Logic
b. Alphabetize
c. Grand Duchess, Spider, Free Cell
d. The Factory Deluxe (visual, and sequencing)
e. Memory Challenge
f. Links to all the web sites below
3. Web Sites – Be aware that many have confusing ads or commercials that are not the game
a. CogMed free game: http://www.spaceminespatrol.com/gamepage.html
b. Dual-N-Back http://dual-n-back.com/index.html
c. Web Sudoku http://www.websudoku.com/
d. Daily Word Jumble http://www.uclick.com/client/phi/tmjmf
e. Tangrams http://www.puzzlechoice.com/pc/Tangramx.html
f. Web-based Solitaire (try Scorpion) (see above) http://www.idiotsdelight.net
g. Countdown http://braingames1.aarp.org/countdown.html
h. Games that can involve pre-planning – don’t use trial and error!
i. Rush Hour http://www.thinkfun.com/mathcounts/play-rush-hour
ii. Tower of Hanoii
http://www.dynamicdrive.com/dynamicindex12/towerhanoi.htm
iii. Bloxorz http://www.bloxorzgame1.com/
iv. Flow Free http://moh97.us/flow/
Many of these – or similar products – are also available as apps!