Recently, I read a blog post requesting submissions for the next issue of Math Teachers at Play, so I decided to submit my equivalent fractions post. It was accepted and published - http://letsplaymath.net

While searching my own digital footprint at http://pipl.com, I came across a mention of that submission at http://www.mathteacherctk.com

It is exciting to see how my digital footprint quickly extends beyond the original source of my posts. It is also a constant reminder to think carefully about what I make available to the world.

## Sunday, February 27, 2011

## Sunday, February 20, 2011

### Successful Cure not Symptom Relief

While responding to another post regarding reward systems, I thought about a paper I wrote for my Educational Psychology and Human Development course in 2007. My experiences in classrooms since that time have greatly reinforced the beliefs I expressed in that paper. What do you think?

**http://tinyurl.com/46eo5tz**## Saturday, February 12, 2011

### Does Your Answer Make Sense

The more time I spend subbing in classrooms, the more I am discovering that I had some pretty amazing elementary math teachers in the 1960s. They taught us the whys and the hows. They also taught us to check the reasonableness of each answer. In fact, I remember learning to look at a problem to determine about what the answer would be before solving it.

I think the focus of math instruction in some classrooms is more on accurate calculation and less about understanding numbers, the procedures, and the processes. Last week, I tried using logic to help a 4th grader understand why his answer was not correct. The problem: 258 - 199. His answer: 159. He knew that 199 was only 1 less than 200 and that 258 - 200 = 58, yet he could not understand how that affected his answer. I've also tried to help students think logically about multiplication facts. If they know that 5 x 8 = 40, they should realize that 3 x 8 can't be 36.

While working on equivalent fractions with middle schoolers, they told me that to find equivalent fractions you do the same thing to the top as you do to the bottom. I asked them why I could do that without changing the value of the fraction. Not one of them knew, so I taught them what I had been taught about equivalent fractions. I could see the lightbulbs go on. They understood that when you multiply both the numerator and denominator of a fraction by the same number, you are really multiplying by 1, so the resulting fraction is equivalent to the original fraction. In my own class, I would take the time to write 4/9 x 4/4 = 16/36, and let them talk about it to see if they would discover for themselves that 4/4 = 1.

After watching Conrad Wolfram's TED talk, I believe he is 100% correct - "Stop teaching calculating, start teaching maths."

Computers can do the calculations. Students need to be able to ask the right question, turn it into a math problem, and check the reasonableness of the computer's answer. If we must use multiple choice assessments, perhaps we could check for understanding by posing questions like this:

I have a garden that is almost 38 feet by just less than 32 feet. About how much planting area do I have?

a) 120 ft b) 1,200 sq ft c) 120 sq ft d) 1,200 ft

I think the focus of math instruction in some classrooms is more on accurate calculation and less about understanding numbers, the procedures, and the processes. Last week, I tried using logic to help a 4th grader understand why his answer was not correct. The problem: 258 - 199. His answer: 159. He knew that 199 was only 1 less than 200 and that 258 - 200 = 58, yet he could not understand how that affected his answer. I've also tried to help students think logically about multiplication facts. If they know that 5 x 8 = 40, they should realize that 3 x 8 can't be 36.

While working on equivalent fractions with middle schoolers, they told me that to find equivalent fractions you do the same thing to the top as you do to the bottom. I asked them why I could do that without changing the value of the fraction. Not one of them knew, so I taught them what I had been taught about equivalent fractions. I could see the lightbulbs go on. They understood that when you multiply both the numerator and denominator of a fraction by the same number, you are really multiplying by 1, so the resulting fraction is equivalent to the original fraction. In my own class, I would take the time to write 4/9 x 4/4 = 16/36, and let them talk about it to see if they would discover for themselves that 4/4 = 1.

After watching Conrad Wolfram's TED talk, I believe he is 100% correct - "Stop teaching calculating, start teaching maths."

Computers can do the calculations. Students need to be able to ask the right question, turn it into a math problem, and check the reasonableness of the computer's answer. If we must use multiple choice assessments, perhaps we could check for understanding by posing questions like this:

I have a garden that is almost 38 feet by just less than 32 feet. About how much planting area do I have?

a) 120 ft b) 1,200 sq ft c) 120 sq ft d) 1,200 ft

## Tuesday, February 8, 2011

### I Just Can't Say No

I have thought about writing on this topic, bathroom breaks, for a long time, and I am finally going to do it. As a sub, I come across all kinds of classroom rules and consequences regarding student use of the bathroom. I really try to follow all the rules of the classrooms I'm in, but on this matter I just can't say no. I am aware that the request may be just an excuse to get up and move around, but I understand because I have needed to get up and move around or clear my head with a short walk many times a day during my 30+ years of office work. When I needed a minute to sort out my thoughts, I got up to file a few papers or get a cup of coffee.

I know I can't have a constant stream of students in and out while I'm teaching a lesson. However, if they are all asking to go during that time, I'd better spruce up my delivery in a hurry. When they are working on their own or in a group, I think they should be allowed to make a quick trip to the bathroom. With very few limitations, I think deciding when to use the bathroom should be one of the choices students have in school.

In a video I recently watched, Rick Lavoie detailed some bathroom use rules and consequences he has come across. He mentioned one that kept a whole class in for recess if too many students left class to use the bathroom. Another incident was about a special needs boy who asked to go about the same time every day. When his teacher finally asked him why he didn't go with the rest of the class before recess, he responded by telling her that the adults didn't protect him during that time and how the group of boys always ganged up on him. Rick ended by pleading, "Let my people go!" And I do.

I know I can't have a constant stream of students in and out while I'm teaching a lesson. However, if they are all asking to go during that time, I'd better spruce up my delivery in a hurry. When they are working on their own or in a group, I think they should be allowed to make a quick trip to the bathroom. With very few limitations, I think deciding when to use the bathroom should be one of the choices students have in school.

In a video I recently watched, Rick Lavoie detailed some bathroom use rules and consequences he has come across. He mentioned one that kept a whole class in for recess if too many students left class to use the bathroom. Another incident was about a special needs boy who asked to go about the same time every day. When his teacher finally asked him why he didn't go with the rest of the class before recess, he responded by telling her that the adults didn't protect him during that time and how the group of boys always ganged up on him. Rick ended by pleading, "Let my people go!" And I do.

### Competitors or Partners

I subbed in PE today and observed something quite amazing. We played Cornhole (bean bag toss) with two people to each pair of boards. I told them we were playing to 21 - 3 points for going in the hole and 1 point if it stayed on the board. Fourth graders were first, and I noticed some pairs were adding the scores of both players to see how high they could go. The next group of fourth graders did the same. They cheered as much for their

It was a wonderful example of kids opting out, on their own, of a win-lose game and playing just for the fun of it. I set up a competition and they turned it into a partnership. Score one for those who believe cooperation should trump competition in school.

*opponent*as they did for themselves. I decided to tell the rest of the classes they could score either way. A large majority of third graders, second graders, and kindergartners chose to go for one big number. They didn't even compare numbers with other pairs, and they all had a fantastic time.It was a wonderful example of kids opting out, on their own, of a win-lose game and playing just for the fun of it. I set up a competition and they turned it into a partnership. Score one for those who believe cooperation should trump competition in school.

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