I have referenced several problems and solutions as math teaching methods.
In the fourth grade class in which I taught, each math lesson would start with 10 single digit addition problems which were written across a blackboard. The children were given two minutes to complete them in their math journals. In the next two to three minutes the children were called upon to give the answers. If the child answered correctly, the child got to write the answers on the blackboard.
One day, after putting the children in small groups, I gave each group their choice of one of five word problems. I told them I did NOT want them to solve the problem. I want them to figure out how to solve it. I chose one of the problems and modeled it but I found out that this class was very weak on problem solving skills. I had to incorporate in several practices on problem-solving to rectify this situation.
To teach fractions, I gave them pieces of colored posterboard on which shades were drawn and divided to cut out. This gave the children their own set of fraction manipulatives. They liked using them. I also gave them a fraction bar guide as an easy way to compare fractions. It was difficult to comprehend fractions that way. So I brought my bread maker to class, measured all of the ingredients in front of them, and made bread (it was peanut butter and jelly bread). I did this in the morning and we ate the bread as an afternoon treat. While enjoying it, we discussed the importance of fractions in baking.
Bos and Vaughan (1998) say to “incorporate calendar activities into the daily schedule.” This I always did. We had a calendar monitor, who would hang a number on the calendar and move the cards in the pockets. If today were Wednesday, Wednesday would be taken out of the “Tomorrow will be . . .” pocket and put in the “Today is . . .” pocket. Tuesday would be moved from the “Today is . . .” pocket and put in the “Yesterday was . . .” pocket, and Thursday would be taken out and put in the “Tomorrow will be . . .” pocket. Monday would be moved to the holding box.
One other thing comes to my mind. This was something I witnessed when I was a student teacher. I noticed a role of adding machine type paper tacked up around the room. Every day the teacher would write a number on it to show how many days of school we had completed so far that year. Every number divisible by two had a yellow circle around it, fives had a blue square and tens had a red triangle. We would practice counting by ones, fives, and tens every day. I remember thinking, what a marvelous way to teach!
I wish I had the Fleischner, Nuzum, and Marzola (1987) instructional program at the time I was trying to teach problem-solving. I would have used it to make ‘fill in the blank’ forms for my students with special needs. I would have the children use it as a guide to word problem solving. I do not know that I would use Hutchinson’s (1993) strategy, though, because I found it confusing.
In reading Bos and Vaughan (1998), I came across an illustration on page 370 about Sally and her puppies. When I read the problem, my first reaction was that Sally had 12 dogs left. I had to stop and think about what was wrong with this problem. It took me a few minutes to figure it out. It has three problems. 1) Sally has 12 dogs. So she must have had 16 dogs in the beginning. She gave away four, and has how many left? 2) It does not say how many of the 12 dogs are puppies. This took me longer to identify. 3) The question says, “How many are left?” How many what are left? I think this is an awkward problem at best. If we are going to teach children who already have problems in math, we must write the word problems as clearly as possible!
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