Technology in Math

This lesson didn't begin with technology. Initially the students were working with three triangles from tangrams and creating polygons. Five regular polygons can be made with those triangles. They then had to find the area and perimeter of the shapes. The goal is for them to realize that shapes can have the same area but different perimeters (or the other way around). It was harder for them than I had anticipated, but they enjoyed it.




















We ended up writing the perimeters of the shapes as algebraic expressions based on the sides of the triangles. Actually measuring was not working well and this was good practice for them writing expressions. Plus, that pushed some of them to finally realize that the areas of the shapes were all the same. Once they recognized that the sides of the triangles remained the same no matter what shape they created, they were able to realize that the areas of each triangle did so as well.


As we neared the end of the lesson we realized that we needed to look at some of it a bit more deeply. I gave each student some fresh graph paper and asked them to try and create shapes with areas greater than perimeters, perimeters greater than areas, and equal perimeters and areas. (I know we are comparing apples and oranges to an extent here because we are comparing units with units squared, but they had a lot of preconceived notions that needed to be questioned.)

Then I wanted to be able to look at some of what they found together. So I pulled up grid paper on my smartboard.

They drew several different shapes to show how each of the possibilities might look. Some students were just amazed that you could have equal perimeter and area or that the perimeter could ever be a larger number than the area. It was interesting to hear their discussion. Then Mr. B opened up Geometer's Sketchpad with a shape that he could manipulate so they could watch the perimeter and area change. This allowed them to test some theories quickly without having to do a lot of tedious computation (which would have caused them to not test their theories). They were enthralled.

This was the best on-the-fly use of technology I've done all year. I was so glad to have the smartboard and Geometer's Sketchpad at my fingertips. The one depressing piece was that I hadn't originally thought to do these things as a part of the lesson.

Weekly Visit to the Library

Equality of Subject Areas

I teach 5th grade in an area where my students head off to middle school next year. Their middle school treats 6th grade as a sort of bridge between elementary and middle school. They switch teachers, but have limited options about courses. They are still pulled out of core classes for band, strings, chorus, and gifted and talented services. They have lockers and dress out for gym. It's a good transition year for them, in many ways.

In other ways I feel like they lose out because they aren't in elementary school for one more year. At my school (and I know this isn't true for all, or even most, elementary schools) our students have two and a half hours four days a week for language arts instruction (reading, writing, word study). They probably have an hour and a half on the fifth day. They have an hour, at least, for math instruction five days a week. Science and social studies get less time. My students have thirty minutes four days a week for each of those, at best. Occasionally we'll spend more time on science or social studies when we are really engaged in something. I feel that my students have to be able to read, write, and do math in order to be able to truly understand social studies or science. So I don't have any concerns about how we spend our time (although I love science and social studies and would enjoy spending more time with them).

However, next year they'll have the same amount of time for math class, social studies class, science class, and English class (which will include reading, writing, and word study). What a switch for them! If they remained in elementary school they would still have a greater focus on language arts and math.

This is yet another time where I think tradition and convenience determine how we handle instructional issues. I wonder if one of the reasons we see so many concerns about young people and reading is because of the small amount of attention we give it after elementary school. Does it truly make sense to value every discipline equally? And equally for all students?

Traffic Jam

A couple of people have expressed interest in the activity in the Wordless Wednesday pictures. The activity is called Traffic Jam and I found it on a website for team building activities.

Use the duct tape (or masking tape) to make a starting pattern on the floor.

Have the participants stand in the boxes of the pattern: half of the group faces right, half of the group faces left.

Explain the task: Using only legal rules, people on the left side must end up on the right side and the people on the right must end up on the left.

Legal Moves

A person may move into an empty space in front of them.

A person may move around a person who is facing them into an empty space.

You CANNOT:

Move backwards.

Move around someone facing the same way you are.

Make any move which involves two people moving at once.

I didn't use duct tape, but we put the pieces of construction paper on the floor. That allowed us to try it first with just half the class (both halves tried it in different parts of the room). Once they were able to do it several times we took it out to the hall to have the entire class do it. That was at the beginning of the year. I do team building activities all through the first week to emphasize cooperation and to foster community. We've done it again now as a part of math. We've looked at how the pattern works and how to explain it mathematically.

It's my favorite of the team building activities that I do and I was thrilled to be able to come back to it.

Wordless Wednesday

Traffic Jam - attempting to move students from one end to the other. They can only jump past one person at a time and can only move the direction they are facing. Very challenging!

Marshmallow Madness

For details of the story, check this out.

Authorities on Education

Every school day I receive an email from ASCD (Association of Supervision and Curriculum Development) with a collection of newspaper and magazine articles. The email includes links and brief summaries of the articles. A year ago it was something I looked forward to in order to keep up with what was happening in education around the country and around the world.

In the past few months I've noticed that I haven't kept up with reading these emails. I finally realized that I would rather spend time with all of the feeds to my reader than to skim through that email. (Of course, the amount of time for those two activities is nowhere near equal.) The authorities on education I turn to now are classroom teachers, like Dan, Doug, Woody, Ruth and Stacey, Tree, Organized Chaos, and Christian, or administrators, specialists and consultants, like, Tim, John, Wes, Chris, and Alice, as well as some big names in the field like Deborah Meier and Diane Ravitch.

The people I read now aren't journalists, they are educators. They know that of which they speak. Who better to be reading to keep up to date with the state of my profession?

100th Day of School

Creating time lines of 100 years in U.S. history.















Things that measured 100 of some unit (centimeter, pounds, etc.)
















Number sentences that equal 100 in a variety of ways (with 2, 3, or 4 operations or using 3, 4, or 5 digits).


Wordless Wednesday (mostly)

Good Nutrition, Good Economics

A study recently found that good nutrition for young children (infants and toddlers) affects their future earning potential. The study began in the 1970's looking at children in Guatemala. Researchers looked at these groups twenty and thirty years later as adults to determine the effects of a nutritional supplement program.

They found that the adult males in the group who had been given the supplement were earning 46% higher hourly wages than the others.

Surprisingly, however,

But surprisingly there was no similar divide in school performance or cognitive test scores.

Does this mean that good nutrition promotes physical strength which helped these men make more money and does nothing for intellectual ability? That seems highly unlikely, but why these results? Was there a reliable way of assessing school performance? What sort of cognitive testing was used?

On a final note, the researchers asserted that their study suggests that societies need to ensure that children are well fed for economic reasons.

"Improving nutrition in early childhood led to substantial increases in wage rates for men, which suggests that investments in early childhood nutrition can be long-term drivers of economic growth," they conclude.

It always comes down to money.

Super Bowl - Quite a Test

The New England Patriots lost their first game all season last night. I know, that's not news to anyone. But it's got me thinking. After an almost perfect season, losing one game has meant that people have called the Patriots' performance disappointing or a failure. This one game, just a few hours, has changed many people's impressions of the team. Is that reasonable?

We seem to do the same thing to our students with standardized tests. One bad day, a few hours of sub-par performance, and a child can be labeled negatively for some time. Their scores on a test often are viewed as more accurate, exact, and important than anything their teachers might know about them. All the anecdotal notes, classroom tests, and other assessments carry less weight.

Our students, at their young ages, aren't ready for a Super Bowl of standardized tests.

Looking for Advice

I posted today on This Must Be Thursday, a blog I co-author with a close friend and colleague. I wrote the post for the cathartic qualities involved in getting emotions out on the page. However, in the process and since I've been mulling the big questions in it. And I'd love to know what others think.

The main questions were

So, what is my responsibility? Should my students be completely unaware of issues I face? Should they know if I'm having a bad day? Does their age matter, older students being more able to deal with understanding their teacher's mood swings or such? Is it my job to teach my students well regardless?

I haven't really been able to figure out where I stand on this and I'm hoping for some thought-provoking ideas.