The Most Popular Spot in My Classroom: Who Tall Are You?

March 27, 2014

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At the back of the room, near the back door, is this brilliant height chart, titled “Who Tall are You?” It’s the most popular place for students in my room. Sometimes when I go out for tea at break times, I’ll return to see some young people have slipped in and are crowding around it. Here’s a link to a good quality image of it. “I’m as tall as Beyonce!” one person squeals.

Every once in a while students will be as tall as someone they don’t know: some of the celebrities now seem a little dated (singer Charles Barkley, for instance) and others are just people my students haven’t heard of yet (such as Alexander Pope).

Since I bought it about five years ago I’m having trouble finding somewhere to buy another copy. But I was thinking today that students could make one of these for display. They could have one featuring their classmates (and teachers?) and heroes of their choice. I reckon my current classes would include more sports people than the original chart.

I’m as tall as George Clooney. If I was making a new chart I would be sure to include Jensen Button, since I am also the same height as him. If you know your height in centimetres, please leave a comment telling us “who-tall” you are!


Building Collaboration Using Changing Partners Activities

March 6, 2014

A few classes needed to revise at the end of teaching units and I wanted them to collaborate while they did so. I printed off a class set of these small checklists with the first names of everyone in the class.

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I also printed some review questions onto colourful card. I separated my tables and spread the questions out over the tables, with two or three on each table. I put some tables facing the wall or the windows so that pairs of students would hopefully focus better on just their partner and the question at hand.

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I gave each student a name checklist to glue into their notes and displayed these instructions.

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From time to time there were not two students looking for new partners at the same time. As a result, sometimes they would have to work in a group of three. Other times there was one person who had to wait a minute to start their next problem. However, this didn’t happen too much and overall I would say that the students did a lot of work. Sometimes in a revision lesson such as this one, students get bored and lose momentum. Not so during this lesson. They stayed on task until the end (80 minutes later) and completed loads of questions. In the last few minutes of class we checked their work as I displayed the answers on the board.

 

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I have tried this with a few classes now and it has worked well every time. It goes most smoothly when the class size is 20 or more. Though I did try it one day when lots of students were at a field trip and I only had seven learners. That still worked but it was a little harder for students to begin and end questions at the same time as others. it devolved into mixed group work instead.

One time I tried this in my class that has a wheelchair student. This also worked smoothy. I positioned her in a place where she wouldn’t be bumped by others walking by. From time to time I prompted students to go over to her since she can’t come to them.

Some tips for myself and others to make this work well:

  1. A class size of 20 or more works best.
  2. It works best if you have enough tables to have at least two empty tables at the start for the first students who finish and find new partners to move to.
  3. Having three questions on each table means students can sit down at the same table a second or third time with different partners and solve different questions.
  4. Make sure the questions are numbered (or lettered) and students write these down as they solve. Then sharing the answers becomes easy.
  5. Mixed revision from several units of study can be done this way. Just mix up the questions around the room.

Do you have ideas about helping students collaborate in math(s) class?

 


Peer Assessment: The “Production Line”

February 17, 2014

My grade 9 students did an individual investigation last week and I wanted to involve them in the process of marking it. I heard about a peer assessment structure called the production line from a colleague last year. In brief, the students mark each other’s work in groups, and each group concentrates on one aspect of feedback. The assignments travel around the group, gaining lots of detailed feedback.


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Preparation

The investigation task already had an assessment rubric. It is based on the MYP year 4 criteria. The rubric focused on Investigating Patterns (MYP criterion B) and Communication in Mathematics (MYP criterion C). I divided the task specific criteria into themes – five in total:

  • B1: Finding and stating patterns
  • B2: Problem-solving techniques
  • B3: General rules
  • C1: Language and representation
  • C2: Reasoning

The Lesson

I rearranged the tables in my room and assigned groups of three students to sit together. I gave each group the details of one of the criteria. An example is shown below (and you can get them all in the investigation file).

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I had some instructions on the board (shown below) and we talked about what we were going to do. I had students help me staple an extra sheet of paper to the back of each task so that we could use it give feedback.


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I gave each group three tasks and asked them to read them, as a group, one at a time. Then they were to discuss the criterion and give some feedback. When they were finished with a task, I passed it on to another group.

Reflection on the Lesson

Since the rubric was already set up for this task, the preparation was quite easy for me. Making a task-specific rubric is a job that can take some time! Thankfully it only needs to be done once.

The number of criteria I wanted to mark didn’t match the number of groups I made in the class. I opted to have three criteria marked by two groups each and two criteria marked by one group each. This turned out to not work very well. The repeated criteria groups finished all the class tasks much more quickly (obviously!) and the other groups had much more to do. When I realised this, I asked two groups to take on a different criterion so take up slack from the inundated groups. Next time, I need to think more carefully about this. I didn’t want to make bigger groups because I felt like they would not work together well. In that case, I should have more criteria so that each criterion is only assessed by a single group.

I just managed (in 80 minutes) to get all the tasks marked by all the criteria groups. Next time I will not need to explain the production line in as much detail and I expect it will be more comfortable in terms of time.

The feedback that was given was extensive, though, I think I need to talk with the students about what the criteria is looking for. I can see the value of a class discussion about what constitutes good reasoning or communication or pattern stating.

The students gained a much more clear view of what criteria they are marked against. (The same criteria are in use throughout MYP maths.)

How do you use peer assessment in your classroom?


Algebraic Fractions Quiz-Quiz-Trade Activity

December 13, 2013

One of my classes of students sat an exam lately and I realized they need more practice with adding and subtracting algebraic fractions. There were a collection of misconceptions on the exam, including not taking a common denominator, trying to cross multiply, and cancelling incorrectly. I made a set of cards (split over two files) to use to help practice this tricky manipulation.

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In this quiz-quiz-trade activity, students start with one question each and make sure they can simplify it. I give them a few minutes to check with their partner or with me. My students like to use their mini whiteboards because it lets them change any errors easily.

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Then they get out of their seats and meet someone from another table. They take their mini whiteboards (or their notebooks) with them. Meeting someone else, they quiz each other. After they are satisfied that they both got their questions correct, they trade cards, thus leaving with a different card then the one with which they arrived.

While the students are quizzing each other, I am able to circulate and address misconceptions. The students are quite good at helping each other. After this activity I think they will feel a lot more confident with adding and subtracting algebraic fractions.

When students sit back down, I ask them to do a few of the algebraic calculations in their notebooks so they have a record of what they learned.

I made these cards using Tarsia software, designed for making mathematics activities. Here are two files (pdf) of the cards.

 


One Easy Way to Never Teach a Boring Lesson Again

December 6, 2013

I have discovered that I can’t teach a boring lesson anymore. I really wanted to today. I was tired and it was Friday, last period. My grade 9s always seem a bit too boisterous when I am the most exhausted. Sigh. All I wanted was to sit them down, get them to be quiet, and do some mindless, repetitive task. Unfortunately, I had done one thing at the beginning of the year that ruled out a boring lesson.

I told them never to bring their textbooks to class.

As a result, every lesson has to involve some kind of activity. We have to talk, sort, write, create, classify, or debate. I have no choice but to get them doing and moving. Even when I most want to sit down and supervise them, I rarely can.

We talked about the index laws, then did a quiz-quiz-trade activity to practice simplifying complicated expressions using indices. Then we wrote a few of the “best” examples (the hardest are the best, right?) in our notes. Then we solved a corny riddle using indices. “How do you write a song to knock over a cow?” “In beef flat.”

Not using textbooks in class can be tiring. But it helps me cause active learning.


Exam Preparation Activity: Collaborative Practice Questions

November 27, 2013

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My students are preparing for winter exams. As a review activity we are making our own revision questions. I set up two shared Google Docs: one for revision questions, and one for the solutions. Each student had to make up at least one revision question for everyone and add it to the first document.

Writing the questions requires an understanding of the concepts behind our topic, so this activity let me see what my students understood and how well.

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Students had to say which MYP level their question was. Our upcoming exam focuses on MYP Criterion A: Knowledge and Understanding, which is graded from 0 to 8. We regularly discuss the criteria in class and so students are beginning to become familiar with the descriptions of the levels.

We had a good variety of questions added, and I circulated to encourage some students to fill holes I thought I saw. I urged some students to write harder questions. In the end, the activity is self-differentiating: each student works on problems at the exact right level. And for each student there are harder problems to stretch them, with me providing the stretch for the topmost students.

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As for the solutions document, some students chose to type their mathematics using the (minimally acceptable) equation editor on Google Docs’ Insert menu. Others worked on their mini whiteboards and then took photos to upload to the document.

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After students had made at least one question, I encouraged them to go on to make another, harder one or to answer the questions of their classmates. I assigned as homework to work through all the questions in preparation for our exam.

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What exam preparation strategies work for you and your students?


Make Your Own Normal Distribution Questions

November 1, 2013

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Today we were building our familiarity with the normal distributions. I had a scan of a textbook page with lots of normal distribution sketches, like the one below. I copied them onto yellow card and cut them out, discarding the textbook’s instructions and numbering.

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Each student got a sketch and I asked them to make up a normal distribution question to go with it. Here are my instructions. Students were working on their mini whiteboards.

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The students got out of their seats to solve other their classmates’ problems. There was a lot of collaboration and those who found writing the question hard got plenty of input from their peers. I was free to circulate and able to clarify some important ideas about continuous distributions and the appropriateness of the normal distribution as a model.

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I was impressed by the questions’ variety and ingenuity.

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I don’t think I emphsized thoroughly enough that students need to specify that the data they have chosen to write about is normally distributed. However, students were able to solve a wide range of questions, some more difficult than others.

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This was definitely much more successful than a page of textbook questions!

 

 


Collaborative Talking in Math Class

October 8, 2013

For the next eight weeks I am participating in Exploring the MathTwitterBlogosphere, a project designed to help math teachers meet others in the cyber community we call home. (It is still a good time to join in, if you haven’t yet.)

Mission 1 is to write about what makes my classroom my very own. One thing I prize and make sure I develop in my students is their ability to communicate with each other about their math. I have been doing more and more discussion-based activities in lessons. I want them to talk about their conjectures and developing ideas. It is rare that my students are sitting in silence. They are usually discussing with the person next to them. Often they are moving around the room, talking to others. Even when we are doing “boring” practice questions they are talking.

umar remi probability never sometimes always true

Here two grade 12 students are discussing probability statements that may be never true, sometimes true, or always true. They had to go meet as many others as they can, discussing the statements on their cards, and each time trading cards. Then they go off and meet another person. (This is a quiz-quiz-trade activity.)

To help students communicate with each other, I have mini whiteboards (MWBs) and pens on each group of tables. Students love using them because they can quickly explain their thinking. They feel more free to make mistakes on the MWBs and to help and comment on each other’s work. Since having them always available, I have noticed a big increase in how much students help each other and talk about their thinking.

With the MWBs it is also easy to share the thinking of one or two students with the rest of the class. In another probability lesson, I asked students to visualize and then draw what they thought a certain probability distribution would look like. Then I brought six of the MWBs up to the front to discuss with the class their common and distinctive features. In the end, our discussion focused on just two of the graphs made by students.

fibber's game probability distributions

All this constant discussion helps my students clarify and solidify their developing ideas. This makes my classroom unmistakably mine.

What makes your classroom unique?


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