My Students Are Having Difficulty Memorizing Those Dreaded Math Facts!

Many of my college students come to me without knowing their math facts. Some do, but most do not. Since we use calculators in the class, it really isn't an issue.  It just takes those students longer to do a test or their homework. One day, the students in my Basic Algebra Concepts class (a remedial math class) were playing a math game to practice adding and subtracting positive and negative numbers. We were using double die (see picture) where a small dice is located inside a larger dice. (I have to keep an eye on these because they tend to "disappear." The students love them!)  I noticed one of my students continually counting the dots on the die. He was unable to see the group of dots and know how many were in the set.  It was then that I realized he could not subitize sets. (to perceive at a glance the number of items presented)

Subitizing sets means that a person can look at a grouping or a set and identify how many there are without individually counting them.  (i.e. three fingers that are held up)  When a child is unable to do this, they cannot memorize math facts since memorizing is associating an abstract number with a concrete set.  Many teachers as well as parents fail to recognize the root cause of this memorization problem.  AND no amount of practicing, bribing, yelling, or pulling out your hair will change the situation.  So what can you do?

First of all, the problem must be identified.  Use a dice and see if the child must count each dot on each face. Try holding up fingers or laying out sets of candy (M&M's - yummy!) or using dominoes. Put five beans in a container, and ask the child how many are in the box. (They may count them the first few times.)  Take them out, and put them back in.  Ask the child again how many there are.  If, after several times, s/he is unable to recognize the set as a whole, then s/he cannot subitize sets.

How do you help such a child?  If you have small children at home, begin subitizing sets by holding up various combinations of fingers.  My youngest grandson just turned four; so, we worked on holding up two fingers on one hand and two fingers on the other; then one and three fingers, and of course, four fingers. I also like to use dominoes. They already have set groupings which can be identified, added, subtracted, and even multiplied. A dice is great because the child thinks you are playing a game, not doing math.  Roll one dice, and ask the child to identify the set of dots. Try the bean idea, but continue to change the number of beans in the box.  My grandchildren love the candy idea because they are allowed to eat them when we are done.  (All children need a little sugar now and then even though their parents try to control the intake.  I love being a Grandma!)

Gregory Tang has written two wonderful books for older children, The Grapes of Math and Math for All Seasons, which emphasize subitizing sets. At times, I even use them in my college classes!  I was fortunate to attend two of his workshops presented by Creative Mathematics. He not only has a sense of humor, but his books can be read again and again without a child becoming bored. Check them out! 

Is Homework an Essential Part of School?

Dictionary.com defines homework as "schoolwork assigned to be done outside the classroom (distinguished from classwork)", but is homework beneficial? Teaching on the college level, I see many benefits to those students who have been required to complete real homework in high school. Here are just a few.

1) Homework can improve student achievement. Studies show that homework improves student achievement in terms of better grades, test results, and the likelihood of attending college.

2) Homework helps to reinforce learning and to develop good study habits and life skills. Homework assists students in developing key skills that they will use throughout their lives, such as accountability, self-sufficiency, discipline, time management, self-direction, critical thinking, and independent problem-solving. Homework assignments given to students actually help students prepare for getting a higher education degree. In fact, the more time a student spends honing his skills, the higher his chances are to enter the University of his dreams or later acquire the work he always wanted to do.

3) Homework can make students more responsible. Knowing that each homework assignment has a specific deadline that cannot be postponed makes students more responsible. It requires grit (perseverance), teaches them time management and causes them to prioritize their time for academic lessons.

As you read this list, I know there are many of you, especially those who have small children or teach younger children, who disagree. I am not here to argue about whether homework is appropriate in the lower grades, but I do want to advocate real homework on the high school level. When I say real homework here is what I mean.

In high school, students might finish their homework in the hall right before class and still earn a good grade; that just isn't possible in college. Homework may be due on a certain day, but it is acceptable if it is turned late. This typically doesn’t float on the college level. In high school, a student gets to the end of a semester and needs a few more points to pull up a grade because of missing or incomplete assignments; so, the student asks the teacher for extra credit work. Extra credit does not exist on the college level! You do the work you are given when you are given it!

I teach college freshmen, many who are woefully unprepared for the academic rigors and demands that are expected. For every one hour students take in college, they should expect two hours of outside work. In other words, if a student is taking 12 hours, they should expect to spend 24 hours on homework (12 x 2).  Of course this formula doesn't always work perfectly, but it is a good starting point. Usually, college freshmen are in disbelief that they are expected to spend so much time on work outside of class. In reality, they should expect to spend as much time on homework in college as they would at a job because college is a full time job!

Help, we're sinking!

When I hand out my syllabus, many of my freshmen are astonished when they discover the amount of homework I expect and require them to do (readings, papers, on-line research, projects, etc.) AND to compound the problem, many instructors (including me) expect it to be done and handed in on time! Unfortunately, several students have to test the waters to find out that late papers are not accepted.

For those college students who've had little real homework in high school compounded by teachers who have allowed it to be turned in late, those students are aboard a sinking ship that is leaking fast! Sadly, those are the 2-3 students who fail my required class and have to retake it the next semester.

So, as you can see, the decision to agree with or disagree with assignments is really up to the student, but also they need to remember that the learning institution they attend has rules in place regarding assignments. And if homework is assigned, then it will need to be completed and handed in on time, or the impact on the final semester grade will certainly be negative.
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Want a quicker and easier way to grade math homework? Try one of these two math rubrics. I still use them on the college level, and they save me a great deal of time!