Reading and Writing in Maths: a new version of maths homework

This week I will teach a lesson about estimating to my year 9s. The lesson will be a pretty standard one for me: a sequence of tasks and activities, some whole class items but mostly pair work. The lesson will involve some discussion about how and why someone might estimate the answer to a calculation. I’ll be using a few slides, a puzzle, some problems to solve (sourced from UKMT Intermediate contests), and a plenary about a poor guy whose calculator doesn’t display decimal points in answers.

But it’s the homework I want to talk about here. I plan to set a two part homework: read, then write.

1. Read

First students will read an article from earlier this year about two skiers who allegedly tied for first at the Sochi Olympics. Actually, their downhill skiing times were reported as identical due to rounding to two decimal places.

Two skiers tied for first (image: New York Times).
Two skiers tied for first (image: New York Times).

2. Write

Next, students will access a Google form that asks them three questions for which they need to write at least 300 characters (about 3 sentences). Here’s a copy of the form that you are welcome to answer “for fun”. (My students will be using a private version of this.)

I’m excited to see what students write in response to the third question: other examples (outside sport) where rounding of a measurement makes a crucial difference.

I’m interested to see what my students think about being asked to read and write for their maths homework. After reviewing literature and reflecting on my practice last school year, I decided to try a whole range of different homework options this year.

Our school offers the IB diploma for the final two years of secondary school. The maths courses each contain a 20% internal assessment that is a written report. So part of my interest in reading and writing in maths is to prepare students better for writing in maths during the IB diploma.

Have you tried out reading and writing activities in mathematics classes? Please tell me about it in the comments.

Reading Notes: The One Minute Manager

When I read I usually take some reading notes (in Evernote) to help me retain the main points and some learnings. I thought it might be a good idea to start publishing these in an occasional series, in case they may be helpful to anyone. They are unedited; just notes that I take while reading about what struck me. There won’t be any commentary, just lots of bullet pointed ideas. Let me know if they are useful, interesting, or both.

The One Minute Manger by Ken Blanchard and Spencer Johnson

“The best minute I spend is the one I invest in people” (63)

“People who feel good about themselves produce good results” (19)

One Minute Goals
1. Agree on your goals.
2. See what good behavior looks like.
3. Write out each of your goals on a single sheet of paper using less than 250 words.
4. Read and re-read each goal, which requires only a minute or so each time you do it
5. Take a minute every once in a while out of your day to look at your performance, and
6. See whether or not your behavior matches your goal.

One Minute Praisings
1. Tell people up front that you are going to let them know how they are doing.
2. Praise people immediately.
3. Tell people what they did right – be specific.
4. Tell people how good you feel about what they did right, and how it helps the organization and the other people who work there.
5. Stop for a moment of silence to let them “feel” how good you feel.
6. Encourage them to do more of the same.
7. Shake hands or touch people in a way that makes it clear that you support their success in the organization.

At first, praise things that are approximately right, and help people move towards desired behaviour.
If, instead, we leave people alone and then punish them when they don’t do exactly the right thing, then they start to do as little as possible.

One Minute Reprimands
1. Tell people beforehand that you are going to let them know how they are doing and in no uncertain terms.
the first half of the reprimand:
2. Reprimand them immediately. [reprimand the behavior only, not the person or their worth]
3. Tell people what they did wrong – be specific.
4. Tell people how you feel about what they did wrong – and in no uncertain terms.
5. Stop for a few seconds of uncomfortable silence to let them feel how you feel.
the second half of the reprimand:
6. Shake hands, or touch them in a way that lets them know you are honestly on their side.
7. Remind them how much you value them.
8. Reaffirm that you think well of them but not of their performance in this situation.
9. Realize that when the reprimand is over, it’s over.

Never save up negative feedback, always give it immediately and in very small doses.
Definitely don’t have surprises at performance management time.
“When you ____, I feel ___.” Then reaffirm their worth.

“We are not just our behaviour, we are the person managing our behaviour.” (93)

why does it work?
“the number one motivator of people is feedback on results” (67)

“feedback is the breakfast of champions” (67)
there would be no point playing golf in the dark; people need to know how successful they are being

“most companies spend 50-70% of their money on people’s salaries. And yet they spend less than 1% of their budget to train their people” (64)

Factors Using Multilink Cubes

My year 8s (twelve year olds) have been learning about multiples and now it was time to talk about factors. Some of them have not got all their times tables memorised, which presents some difficulty for our unit of work on factors, multiples, and primes. So my teaching assistant and I doled out the multilink cubes and I asked them to make rectangles. I wanted to know if any number of cubes could be made into a rectangle shape, fully filled with cubes (no gaps).

2014-09-02 11.53.39

After the students played with this for a while, I started making a list on the board of all the sizes of rectangles they had made. Then I asked, which numbers of cubes can be made into more than one shape of rectangle? Above are two rectangles with 8 cubes and below are three rectangles with 12 cubes.

2014-09-02 11.53.36

 

Next I introduced the idea of a factor by talking about the sizes of the rectangles and after some discussion we listed all the factors of 12 using the rectangles in the picture above.

After that, students made their own lists of all the factors of some numbers of their choosing. My assistant and I went around to their tables, asking if they were noticing anything. Using their results, we made a table on the board of all the factors of the numbers from 1 to 15 and talked about what they noticed.

Top on their list of noticings were: 1 is always a factor of every number and the number itself is always a factor. These were not obvious statements to my students. We discussed why each was true by talking about making a long skinny rectangle of 1 x __ for any number.

Next lesson is going to be about prime numbers, so I hope that their next noticing is that some numbers have a lot more factors than others.

Do you use multilink cubes in your lessons?