Links Picnic #2

Links Picnic is an opportunity for us to share things from around the web that help and inspire maths teachers. Here are my picks. Please add yours in the comments section. You can leave a link to your own Links Picnic!

–A nice world clock that can be used between lessons or during registration. It includes world statistics that are continuously updating.

—WiseStamp for an interactive email signature.

–The $2 Interactive Whiteboard. I’m calling this the medi-whiteboard, since I already use mini-whiteboards.

–An article I’m reading by Alfie Kohn about homework, entitled Do Students Really Need Practice Homework?

–Some ideas for displaying student testing data in the classroom. How motivating is this, I wonder?

–I am looking for an app or program that helps me organise my to-do lists over my mac at home, PC at work, and phone (Android). Pocket Informant does look useful, but is just for my phone. Do you have a suggestion?

What links have impacted you recently?

Tessellation

I learned something from the year 7 textbook recently! I was surprised that I had never thought about these two facts (as shown in questions 2 and 3 above.

And the answers were there, staring at me from the page. I would love make this into an activity where the questions build:

  • Draw a triangle that tessellates. And another. And another. Do all triangles tessellate? Prove it.
  • Draw a quadrilateral that tessellates. And another. And another. Do all quadrilaterals tessellate? Prove it.

What have you learned lately? Have you been surprised?

Links Picnic #1

Links Picnic is an opportunity for us to share things from around the web that help and inspire maths teachers. Here are my picks. Please add yours in the comments section. You can leave a link to your own Links Picnic!

Are you making any of these four mistakes with your differentiation? Two of these items make me think setting students by ability might be wrong. (And those thoughts are making me nervous.)

Using Evernote as a filing system for public speaking. I wonder if this would work with teaching.

A new blog I am following is Under Ten Minutes. The videos posted there show you how to use an item of learning technology in less than 10 minutes. Today I learned how to use pivot tables for student data analysis.

The Centre for Innovative Mathematics Teaching (CIMT) pages contain a complete scheme of work, texts, and activities for 5-18 year old learners! What a treasure trove.

What links have impacted you this month?

Ways Students Learn

Do you remember how you learned maths in school? And do you remember if it was effective? As I teach I test out many different strategies, activities, and ideas. I am looking for methods that help everyone learn maths. Are some methods better than others for everyone?

There are certainly some students who learn well by listening to explanations and copying examples. I know that students can be trained to work this way and I have worked in schools where this got very good results. But is everyone able to learn this way? Can all students be trained to learn this way? Ollerton and Watson think not, in their book Inclusive Mathematics 11-18, which I am reading at the moment. (Yesterday I had read to page 7 and was already learning!)

“It is commonly believed now,” they write, “that all learning involves the learner interacting with the environment through experience and making sense of those experiences personally and through communicating with others.” So my job evolves from example-giver to activity-designer. I need to provide sense-making tasks for students to experience and communicate their ideas.

I struggle sometimes with knowing how to make these activities. I enjoy making different types of activities, but often I just pick an activity I like, somewhat randomly. But the key is to look at the underlying mathematical structure. Maths topics are often about classifying–and so sorting and classifying tasks will expose those ideas. Maths is frequently about justifying, so I need to ask questions that ask students to back up their ideas. I hope that Ollerton and Watson discuss task design in more detail. (I am still only on page 10.)

What thinking drives your task design? How do you decide what activities to give to students?

Maths as an Art

I am reading Inclusive Mathematics 11-18 by Mike Ollerton* and Anne Watson (my two biggest maths education idols?). I’m only on page 7 and my ideas are being challenged and shaped. There are a lot of fthings they say that I believe in principle but find hard to apply in the classroom.

Maths (as a school subject) should be something to do, they argue. I agree completely. Often maths is viewed as a body of knowledge that others have created that we need to learn (and memorise). In this way maths skills can be seen like a checklist to master. Some of my lessons have this theme: the aim of the lesson is to master the skill of finding one amount as a percentage of another. But Ollerton and Watson contend that thinking mathematically and doing mathematics are what maths is all about. Memorising (“learning”) techniques is somewhat useful–because of future maths study or work-related skills or everyday numeracy. But the goal of thinking and doing mathematics, I believe,  is to have a more mathematical mind, to be more logical, and to be a beautiful thinker.

In this way studying maths at school could be similar to studying art or music. Students take music, art, or drama in order to appreciate these realms of life. They broaden their minds through artisitic expression. All students are painters or actors who have something to learn in school performing arts classes because they are developing their creative talents. Only a small proportion of the students go further with art or music–and the same is true of maths (though perhaps the percentage is higher?). But the arts and maths are still valuable to those students since their minds and creativity are improved.

So how can I teach maths to be more like an arts subject? I can do this by focusing on maths as a process to be explored rather than memorised. I can also give problems which allow students to investigate and apply their mathematical ideas. Ollerton and Watson say that students “sometimes learn more when plunged into a complex mathematical situation”–so I can avoid giving five simple examples then asking for skill practice. I can develop activities that make students think about why things work.

Would you say you teach maths like a list of skills to be mastered? Or do you focus on “doing” mathematics?

*Ollerton seems to have no website. Take me on as your apprentice, Mike, and I will create your website in return!

Glogging

I know it sounds as thought I am coughing on you, but no, glogging is a new technology that another teacher suggested to me today. Have a look at glogster.com for example. A glog is a poster page with graphics, sound, videos, and links. It looks pretty cool. And apparently some teachers use it too. More investigation will ensue. Have you ever heard of glogging? Or used it in school?

Marking–That Most Hated of Activities

I may have already mentioned that marking is something I find difficult, and that I also intensely dislike. As the school year ended and I was looking back on my marking especially I felt the same wistful longing as every year, “Maybe next year I’ll get it right.” I know how useful it can be to students and how important it is for them to know how they are doing and how to improve. So I feel that sooner or later I need to get out of my marking misery. So here’s an inventory of what went well this year and what could be improved.

What went well:

I made a lot of progress in terms of what I was recording in my (paper-based) mark book. I was more careful about writing in homework marks and I made more of an effort to collect these during class time when the students were on task with something. I was better at following up on students who didn’t do homework and applying the consequences I say that I will.

I was helped by a better way of recording missed homework in my mark book. I had a column on a separate page from the weekly homework columns where I recorded the dates of the first missing homework and any follow up offenses. Then I could more easily read these off, instead of trawling through the weekly columns. And I had a record there of detentions given as well. This made communicating with the Heads of Year or parents a lot easier.

I collected the books more regularly and more proactively. In some classes I collected them even when I thought I wouldn’t have any time to mark them, since on a few occasions this led to me spot checking and stamping a few books.

Still needs improving:

I have both paper-based and electronic mark books and this is confusing for me. My husband and I have talked about getting me some kind of hand-held device that I could use in my classroom tours when I am checking homework, but I don’t have one (yet?) and so paper still seems better. But electronic is the way of the future, and can provide data that is useful and searchable. It’s obvious to me that I need to move more electronically, but it just doesn’t seem convenient enough yet. I would love to survey other teachers about what they do electronically and how it is set up.

When I get busy, marking pretty much stops. I hate it and so I put it off and it is so easy to procrastinate from it completely. In my temporary job at the end of this term, I marked for the first half term, then didn’t bother. It was near the end of term and there were very few repercussions for me. I am ashamed of my dislike of marking and I want to know how to make it better!

I don’t always leave very useful comments for students. I am just moving to a school where the policy is that only comments are given in the lower school (years 7-9) and so I will need to improve my comment-making. Students deserve useful feedback.

I keep a lot of things in my head, especially those things I end up writing on reports. I wish I had a good way of recording them. My memory is out of space now and I am concerned that I won’t remember what I need. My students don’t have a great idea of how to improve because that’s not communicated to them very well. This could be done in lessons, not just through marking.

Ideas for next year:

I have a little stamper that says, “Lesson objective achieved” with my name and a smiley face and a thumbs up. I need to start using this at the end of lessons—work my way around the room checking work and seeing what I can praise.

I think it’s time to complete the transition to a fully electronic mark book. I hear a rumor that I might get a tablet laptop from the new school. That might make it all the more possible!

I have always talked about teaching students to peer assess. I know that this helps them gain an understanding of what makes good work. And, in the context of this discussion, it makes marking easier, and also more meaningful for me. It’s easier to comment on a peer’s assessment by saying what I agree with. And I can add comments that help a student assess better next time, as well as letting the student know what they can do to improve their homework.

The name of this blog reflects how much I value my own feedback loop, and so now I need to finally give the students the same positive feedback experience that I thrive on.

Students Learning Techniques

Exam practice: a necessary evil; working through loads of past papers. Students need to be familiar with the types of questions and what they mean.

But before this, when students are learning techniques like adding fractions, do they need to do repetitious exercises? Do they need to practice twenty (or more) simple fraction addition questions? In my summer reading book, Developing Thinking in Algebra, the authors argue that students can gain fluency with a technique not by practicing it but by putting it into use. They state that another maths education writer argued that “in order to develop competence and fluency it is necessary to divert your attention away from what you are doing, rather than into it” (a summary of Caleb Gattegno in The Science of Education Part 1: Theoretical Considerations). This reminds me of what my department was trying to do with their year 7 fractions unit. Instead of the repetition of the adding fractions section in the textbooks, I used an nrich activity that investigates a fractions question based on adding fractions. Then the students are drawn into a task about whether all fractions can be written as the sum of unit fractions, and while doing their task they practice adding fractions more than enough.

“Learners do a lot of examples in pursuit of a greater goal,” Watson, Graham, and Johnson-Wilder say: and in doing so they gain the skills that will help them later (for example, to make connections with other areas of maths and also at exam time). They also they see when a technique is needed and how it can be used. And this is more valuable than simple, mindless practice.

“Expose the Scaffolding”

Students aren’t mind readers. They can’t hope to understand what I’m looking for in homework, classwork, or group work unless I help them. I’ve received some funny homeworks when I haven’t made my expectations clean; mostly tiny amounts of work that a student thinks is the minimum they can get away with. For example, a sentence when I was expecting a paragraph, or one calculation when I was expecting a whole page. And who can blame them, if they don’t know what to do or why they should do it.

A colleague lent me a booklet of photocopied articles he’s reading about student motivation. “Teachers should spend more time explaining,” one of the articles expounds, “explaining why we teach what we do, and why the topic or approach or activity is important and interesting and worthwhile.” This reminds me of the advice of Paul Muir, one of my first teaching mentors: always “expose the scaffolding”. Make clear to your students why you are doing what you do. For example, he advised me to explain my marking strategies. Or to say why you are giving homework and what purpose it will serve. Explain where the course is going or how today’s work will fit in. Paul said this over and over again–it has been engraved into my memory now.

If we let students in on our planning and organising secrets, they are more likely to complete tasks well. They will know what is expected of them and more often hit the target. And they will catch some of our enthusiasm when we talk about maths.

Dear Mrs A

This term I used Anne Schwartz‘s format for getting feedback from my students. I asked them to write me a letter. I’ve been teaching these students for ten weeks and I wanted to see what their impressions were.

Dear Mrs A,
1. The best thing you did was….
2. The worst thing you did was….
3. I am awesome because….
4. This summer I’m….
From, [name], your favourite student.

Here are some responses from top set year 7 students.

The best thing you did was let us play games.
The worst thing you did was giving us 3 exercises for HW.
I’m awesome because I did well on the fractions poster.
This summer I’m going to Taiwan, Beijing and San Francisco.

I’m awesome because I did well on the olympic stadium project and I learnt a lot about making sums simpler.

The best thing was you letting us choose our seats.
The worst thing you did was giving us a lot of homework.

The best thing you did was help me understand about shapes.

The best thing you did was let us work in pairs and groups.
The worst you did was give us quite a lot of homework.
I’m awesome because I improved my understanding in fractions, algebra and measurements.

The worst thing you did was give us lots of HW that was easy but long.
I’m awesome because I know year 13 stuff and beggining pre calculus and complex number and quadratic formulas.
This summer I’m doing an extra maths course and swimming class.

The best thing you did was giving us lots of practical tasks.
The worst thing you did was making us move the tables and chairs around.
I’m awesome because I went to every math competition, even purple comet and HKMO.

This summer I’m going to read a book of maths given to me as a present.

The best thing you did was to help me understand things when I am confused and made our lessons more interesting.
The worst thing you did was make us play a token game which was quite boring in my point of view.

The worst thing you did is… I really don’t know. You make your own mistakes, like every human.
I’m awesome because… I don’t think I am. I’m just a learner.
This summer I’m going to practise a bit of algebra.

The worst thing you did was give us far too easy work.

The best thing you did was talking for a minute about how people write.
The worst thing you did was not checking our homework.

The students quite rightly pointed out how much homework I gave and that after a while I stopped checking it. Marking is always my downfall. Sigh. I live in hope that one year I will get better at it.