Is Your Email Signature as Nerdy as This?

July 10, 2014

I was reading blogs and came across this wonderful idea for an email signature.

Even if you think you don’t love mathematics, mathematics loves you.
Don’t believe me? Solve for “i”.
9x – 7i > 3(3x – 7u)

How marvellously nerdy! This is from the blog Math = Love.

Is your email signature as nerdy as this?


Circle Theorems Choice Board (A Differentiated Lesson)

June 9, 2014

I had just two 80-minute lessons and their homeworks to help my students learn about the circle theorems. So I put together this choice board for them (here’s a file for you). I had a (not very great) powerpoint with an overview of the circle theorems that they would use as a resource; you could also use a text-based resource or a video.

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I told students about the first theorem, then said they were going to learn about the rest of them. They had to choose a line of three items to demonstrate their learning, horizontally, vertically, or diagonally. They could work individually or in a pair.

It seems that my students preferred the diagonal line from bottom left to top right, since many pairs picked those three items.

The treasure hunt is an activity in the pod outside my classroom with questions and answers scattered around that they have to find and follow in order. (It’s a paid-for item that my school has purchased from Mathsloops.)

The sorting cards are a collection of diagrams that need to be sorted according to which circle theorem applies, then the missing angles calculated. (Embarrassingly I can longer find the file from which I made them years ago. Here’s a card sorting activity I found online that’s a bit different but would work well here.)

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I had two great posters made by students and even had one short story. Two groups made games and one student tried a comic. Read the short story below!

The Life of a Circle

Once upon a time, in a land far away (called England) there lived a circle. This circle’s name was Kevin, his life was endless (pun intended) but his life was not as exciting as he wanted it to be. One day, when Kevin was rolling along the road he didn’t realize that there was a slope in his way. He started rolling down the hill very fast and couldn’t stop himself. “CRASH!!!” When Kevin looked up after recovering from his dizziness, he was amazed by the figure standing in front of him. He looked up to find that a beautiful tangent had stopped him from crashing into the brick wall just meters away from them. He finally spoke, asking her who she was. She replied kindly and softly saying, “My name is Tangentina Tangent, how about you?” Quickly, Kevin pulled himself together and gathered the words to tell her that his name was Kevin Circle and thanked her for saving his life. They both looked down nervously and realized that they had met at a 90° angle. Tangentine said, “You know, it’s a well known fact that circles and tangents become the very best of friends because they meet at a 90° angle. I think that this could be the start of a very very very long and wonderful friendship.” Kevin said, “Tangentina, I am very pleased to meet you but, you have to get your facts straight, it’s tangents and radii not circles. But yes, I am excited a the thought of having a new friend.” Tangentina smiled and took Kevin’s hand and they rolled and bounced off into the sunset.

THE END

(They live happily ever after)

I’m contributing this post to #made4math, a way for maths teachers to share projects in the classroom. It’s hosted by the blog Teaching Statistics.

Do you have a differentiation activity you like?


Mathematics Homework: 26 Good Ideas

June 5, 2014

This week I have been reading, thinking, and chatting about homework. On Monday I posted some doubts about homework and mentioned that I set homework in accordance with the school policy, which at the moment means I assign it after every class and it is mostly routine practice. Today I participated in a Twitter chat about mathematics homework as part of the #eduread group. The idea of the group is that we read an article each week and then discuss it on Twitter and our blogs. This week’s article was “Homework: A Math Dilemma and What to Do About It” by Patricia Deubel. You can read our Twitter chat on the Storify summary.

Meaningful and Purposeful Homework

The main point that hit home for me was there is no use setting homework unless it is both meaningful and purposeful. I sometimes set homework mindlessly and don’t value it much. I am coming to think that homework should only be assigned if there is a clear academic purpose and the task is not just rote practice.

Differentiation of Homework

Also, homework should be differentiated, says our reading. This is a struggle and I would love to hear from teachers who have managed this. I think my main barrier is the time to do it, but I realised that one way would be a homework task with differentiated products. Students would choose their own method of demonstrating their understanding. This is still an idea in its infancy for me and needs more thought.

26 Good Ideas for Mathematics Homework

During my reading and thinking, I made a list of possible homework tasks.

  1. read or outline a chapter (pre-learning)
  2. complete an organizer of a chapter (pre-learning)
  3. write down questions they have about a reading/activity
  4. write/diagram all you know about [upcoming topic]
  5. do a few sample questions and explain the steps
  6. do practice questions (time-based)
  7. answer journal questions about something done in class (ask students what was done and why)
  8. two parts: 1. three problems to check understanding of a concept taught today; 2. ten problems to practice a concept previously learned
  9. draw pictures/diagrams to illustrate a key word
  10. create a concept map
  11. write two problems for others to solve
  12. list the four most important ideas about ….
  13. read and write sticky notes for things you have questions about
  14. design your own learning strategy for a topic covered in class (cards, song, poem, etc)
  15. create a Q&A game
  16. write directions that teach someone else
  17. test corrections: must write why they missed that question, then answer the question correctly
  18. find examples of … at home, in the news, etc; take pictures of … ; then use these in the next class
  19. respond to a thread on Edmodo/other VLE asking a question or sharing an idea
  20. “sandwich” homework: give students the problem and answer and they must fill in the middle
  21. write a summary of today’s class
  22. write a reflection of your work in today’s class
  23. in class, do a notice/wonder activity and generate questions, then students pick one/two to investigate for homework
  24. a project that shows your understanding
  25. adaptive online software such as Khan Academy or MathXL
  26. teacher chooses 3-5 problems, then student chooses another 3-5 from a set

Students’ questions (posted on Edmodo) after reading an article giving English Premier League football standings if only English players’ goals counted

Using Homework in the Next Lesson

Another thing that really struck me started with this quotation: “Homework in the best classrooms is not checked–it is shared.” I was inspired to try to use homework that would generate discussion in the next class. Or it would contribute to the next class’s learning experiences. (Also, I hate checking homework. If the assignment needs to be used for something in the next class then it is kind of “self-checking”.)

Students' sticky notes with a question they had based on their homework reading (pre-learning for an upcoming topic)

Students’ sticky notes with a question they had based on their homework reading (pre-learning for an upcoming topic)

Things to do with homework in class instead of collecting or checking it:

  1. self-assess your homework in terms of effort, understanding, completeness, or accuracy
  2. reflect on which questions were the easiest/hardest and why
  3. find a peer who approached the problem differently than you and discuss our strategies
  4. quiz with 2 randomly selected questions from the homework assignment
  5. get your peer’s feedback on some aspect of your homework
  6. work with a friend to get a best answer to one hard question
  7. give a new problem and ask how it compares to the homework problem(s)
  8. choose the two homework questions that were most alike or most different and explain why you picked them
  9. gallery walk of the results of investigates into notice/wonder questions (see idea 23 above)

More Homework Ideas and Links

I am still learning and thinking over these things. (Sidebar: I love being a teacher because I am always learning. Ten years in and I am excited to be learning about good practice in my profession.) Please share your homework thoughts in the comments or tweet me @mathsfeedback.

Here is a list of the things I read this week while thinking about homework:

 

Please share one good homework idea!


Mathematics Homework: My Dilemma

June 2, 2014

A few months ago I started compiling my viewpoints about mathematics education. What I mean is that I have been using sticky notes to record my beliefs about mathematics education and collecting them on a piece of flipchart paper on my back classroom wall. (Strangely, no students have asked about this. I wonder if they read the stuff on the walls at all??) The viewpoints poster has been a personal exercise to help me clarify my thoughts and see which issues I have strong feelings about.

viewpoints on maths ed 1

I used yellow sticky notes for beliefs I can justify and for which I can provide examples. I used pink sticky notes for issues about which I don’t yet know what I believe. One of these is homework. It seems to me that some people feel quite strongly that homework is bad and should be abolished. Others hold that homework is essential; for some it is even sacred. I have no idea where I sit on this issue, hence the pink sticky note.

viewpoints on maths ed 2

Most of the time, I feel as though my thoughts don’t matter too much because homework policy is determined by the school I work in. If my school says to assign homework, I do so. I usually follow the lead of my head of department in what types of homework I set and how much.

But I think it is time to do some reading around this subject of homework and come to some conclusions of my own. After all, I have strong views about all manner of other things (for example, setting students into classes by ability and acceleration of more able students), and my views have to submit to the policy of the school and my department. So why not form some views about homework?

As a first step, I will be participating in the #eduread discussion about mathematics homework. The plan is to read the assigned article by Patricia Deubel and write about it. Then there is a twitter chat about it on Thursday morning (June 4). (Or Wednesday night if you live in a North American time zone. Or the wee hours of Thursday morning for Europeans…. Maybe Europeans are better off reading the summary afterwards.) Update: The second post in this series about homework is: 26 Good Ideas.

Do you believe in homework?


Famous Mathematicians Choice Board (Differentiation Idea)

May 29, 2014

A few years ago I made a project that I used with my year 7 (eleven year old) students. I introduced it by talking for about two minutes about Blaise Pascal, a mathematician I find personally interesting.

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Then I told my students they were going to choose a mathematician to learn about and it would be their choice how to show their learning. There are nine options for them to produce, and they needed to do three of them which form a vertical, horizontal, or diagonal line from the choice board. (Here is the choice board file.)

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I arranged the nine items so that the lines require some diversity of products. The two times I have used this project my students have responded very positively to the choices. The second time I did it, after they had made their three items, I made larger groups of those who had chosen the same mathematicians to put together a display board of their work. It’s a bonus for me that this project makes for a lot of good display work if you need/want to change your classroom displays.

I think if I did this project again, I might allow more choice on the person as well, perhaps by adding the option, “Choose another mathematician of your choice and have it approved by Mrs A”.

I am posting about this today because I was reading Mr Bigger’s post about differentiation using choice boards. It also makes me think that I should try to use a choice board for a more “meaty” mathematical topic. Has anyone done this before and have an example to share?

 


Lesson: Ferris Wheel Exam-Style Question

May 2, 2014

Sometimes I just want to remind myself and others that not every lesson has to be “special” or involve a game or video. Lessons that are successful are those where students learn to think better and experience mathematics at work. Here is one of those; it’s not flashy, just solidly successful.

It is time to review our work on trigonometric functions in my grade 11 class (IB Mathematics SL year 1). I made this document with an exam-style question closely modelled on recent exams. The question is about a Ferris wheel rotating at a constant rate.

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The first page is the question, which I copied onto half sheets and gave out. These instructions were on the board.

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I told my students to try to work in exam-style conditions for the first step, promising that under the black box on the slide there were other steps we were going to go through with this question. Then when it seemed like everyone had time to attack all the parts of the question, I moved the black box on the slide to reveal the next set of instructions. Students worked in pairs to create their best answers.

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And finally, I gave out the mark scheme (the second page in the document) and we moved the answer papers around so every pair marked answers from someone else.

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We then returned each student’s paper and they got to glue their corrected answer and the mark scheme into their notes.

This lesson mirrors the discussion idea called Think-Pair-Share and provides good exam practice. Students appreciate getting to see the mark scheme and how it applies to a their own and another’s answers.

My lessons are like this a lot of the time. I would say I teach a whizz-bang-special-game-or-video lesson once a week, or less when I’m tired. But I always try to get students talking, working together, and going deep into mathematics.

How much of the time do you teach whizz-bang-special lessons?


Using Exit Slips: an #eduread post

April 29, 2014

My grade 11 class (Mathematics SL year 1) are getting ready for an exam in a week and a half. I was reading this week’s #eduread article about exit slips while they were doing a quiz. I got to the end of the article a few minutes before they finished and I was pondering the last two sentences of the article:

Exit slips are easy to use and take little time away from instruction. Many teachers use them routinely—even daily—and attest to their positive influence on student achievement.

It’s been a while since I used exit slips so I thought, well, there is no time like the present! And I wrote these three questions on the board to use immediately with my grade 11s.

 

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I passed out some small pieces of scrap paper, and voila!, exit slips.

The article mentions four main uses for exit slips. First, to get formative assessment data. My first two questions are of this type. Students give feedback on what they have learned. I now know that my students feel somewhat prepared; the median and modal level was 3. I need to plan more review about trigonometric functions and applications of differentiation.

Secondly, exit slips can be used to have students reflect on their learning strategies or effort. An example question would be “How hard did you work today?” I am planning to use this question soon–it could be illuminating.

Thirdly, the slips can be used to get feedback about my teaching. In the past I have often asked how my pace was during that lesson. My third question today is also of this type. Some students asked for more exam-style questions, several others want me to do tricky stuff on the board.

Last, exit slips can be a place for open communication with the teacher. In the past, I have frequently asked, “What is your foremost question or concern?” This prompt allows students to say whatever it is they want to about mathematics, our class, or anything else. The responses have ranged from useful to hilarious.

This post is for a group of mathematics teachers who read an article and chat about it each week using the hashtag #eduread. You are welcome to join in; our chat about exit slips is on Wednesday night at 8pm in North America/Thursday morning at 9am in Singapore (and the time where you are).

What questions would you ask on exit slips?


Giving More Useful Feedback to Students: an #eduread post

April 24, 2014

How to give better feedback is always a goal of mine. I sometimes (maybe frequently) find it hard to keep up with the pace of teaching, assessing, giving feedback, and reflecting on it. What about you?

Today I was reading a short article titled “How Am I Doing?” with some pointers for effective feedback. Five very useful ideas were presented; have a look at the article to see them all.

2014-04-24 13.56.23

The item that struck me the most was that students need a clear view of where they are heading with their learning and what their learning target is. Phrased in this way, it is a very simple idea and one I have been familiar with for years. However, I have found that at times students think their job in my classroom is to complete the activities I give them. They think that completion of activities is the success criteria. Instead I need to get across to them that their job in my class is to reach desired learning outcomes.

This relates to feedback in that there is no use giving feedback when students think they have successfully completed the task of “learning”. Feedback may seem like giving them more work to do, rather than helping them learn. But if students know their job is to achieve a learning goal. Feedback about progress towards learning goals helps students know how their efforts are leading to success.

In my classroom I am not the best (yet! growth mindset!) at giving indicators of where learning is heading and how we will get there. I was marking student work today and saw this comment (pictured above): “This is confusing because you have not explained what you are trying to do.” As it turns out, that is exactly what I need to hear myself! I appreciated this article as a reminder to expose the learning goals more frequently. And to provide personalised, specific feedback to students about how they are going towards meeting those goals.

#eduread is a group of mathematics teachers that read an article each week and discuss it on Twitter. Here is the blog that organises it. The chat is on Wednesday evenings in the US, which is Thursday morning for me. I can’t always participate in the Twitter chats but I can usually follow along later thanks to the hashtag. Would you like to join us?

Do you find it easy to give useful feedback to students?


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