plenary – In Pursuit of Great Mathematics Teaching

Which is More Valuable: Getting or Giving Feedback?

Students can get feedback from me, their teacher, when I mark their work or talk to them in class.

Students can give feedback to me when I ask them about their learning.

Which is more valuable for student learning? According to an article I was reading today, getting feedback from students is more powerful than giving students feedback. Cris Tovani argues that when teachers obtain feedback from students they can make changes easily to subsequent lessons, and this leads readily to improvement in the students’ performance. Tovani is a reading teacher, so here are a few ideas from me to help get feedback from students.

Three Minute Feedback

I do love this strategy and it’s the only thing I’ve continued doing since the very first teaching I did at university. (Sometimes I forget to use it, though, for months at a time. Does anyone else have this problem, even with great ideas?!) See here for an example when my IB SL students were preparing for a test; see here for an example when students were learning to expand brackets. Here’s one I prepared for my year 9s for tomorrow; they are revising for a test. Tovani says that after she spots the patterns in her exit tickets, she throws them out – it was freeing to read that.

3 minute feedback revision

Looking for Themes in Book Marking

When I take in a set of books (or tests), I jot notes to myself about commonalities among the students’ work to see on which topics they need help. If it’s just a small group of students who need help with factorising, for example, I might invite them all around one table when the class are working on something.

Quick Quizzes

Short quizzes with only a few questions that can be done at the end of class let me know if a concept from earlier is still secure. For example, I gave a four question trigonometry quiz to my year 10s a few weeks ago (and discovered that I need to refresh their memories about the difference between trigonometry and Pythagoras). I would like to get into the habit of using more mini quizzes.

Giving and Getting Feedback

Each of these examples allow students to give me feedback about their learning but they are also a means of the students getting feedback from me. In the case of the Three Minute Feedback, they have the chance to reflect on their learning and identify what they need to do next. With book marking, I have been challenging myself to only write questions to prompt thinking that will help students improve. In the case of quick quizzes, I provide detailed exemplar solutions afterwards for them to see and analyse. Thus students know where they are now and how to improve.

Which do you find easier in the classroom: giving students feedback or getting it? Tweet me (@mathsfeedback) or comment below.

Reflection Time

Last week we had a professional development session with Andy Hind (@andyhind_es4s) about deep learning. One thing that stuck out to me was the value of reflection time in order to deepen learning.

Reflection time for students.
Reflection time for me.

Students need time to reflect on their learning in order to embed it and connect it to their existing knowledge. One strategy Andy used which I will use in lessons was a small picture of a nutshell that popped up about twenty minutes into a session. Andy said, “Tell your partner everything that has happened so far, in a nutshell.”

He said that students should reflect at four points in a one hour lesson. At the beginning (thinking back to the last lesson), after twenty minutes, after forty minutes, and at the end. I scribbled down this time line.

Tomorrow I’m incorporating reflection time into my lessons twice. At the beginning of one of my lessons we are going to recap the last session with the instructions on this slide.

In another lesson I want to ask students to reflect at the end of the lesson, and I’m using the slide below. It’s a feedback structure I have used since even before I was a school teacher. I learned about it from my colleague Richard Hoshino while I was a lecturer at university.

The “3 Minute Feedback” questions always follow the same pattern. The first question is related to today’s lesson and allows me to see if students have succeeded with the objective of the lesson. The second question relates to my teaching. The third one is always worded exactly as above and gives students a chance to share anything on their minds. I like to respond to these via Edmodo after the lesson by giving the class an idea of the proportion of responses of each type and by answering the questions.

I need reflection time in order to become a better teacher. I used to blog more regularly and this was a good method of reflection for me. But Andy also suggested a private reflection journal and I’ve started one this week. I set an alarm for half an hour before I want to go home. I use 15 minutes for writing reflection and 15 minutes for tidying up my desk. I haven’t managed to do it every day this week, but I’m pleased that I have done it three out of the last six workdays. I’m going to either write in my journal or on this blog during my afternoon reflection times this year.

How do you include student reflection into your lessons?

Using Exit Slips: an #eduread post

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.

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?

Laws of Logarithms

My year 11 students are nearing exam time and the last item on our course is an introduction to logarithms. They had just learned the laws of logs and so we finished the lesson with this activity. I put some pink papers around the classroom, each with a requirement.

Each group of students had to use their sticky notes to add one or more expressions to each pink poster. I was quite impressed by their responses and it was clear they had understood our lesson objectives.

A Pythagoras’ Theorem Open Question

An open question like this one:

is easy to pose,
is easy to understand,
can lead to lots of practice (if that’s your goal for the students),
can be kept simple or extended to suit lots of students,
can lead to an interesting discussion,
can lead to a generalisation.

I used this with a year 11 class that are revising for their Foundation IGCSE exam. I asked students to come up to the board and sketch some triangles that fit the criteria. Some triangles had 10 cm as the length of one of the shorter sides. Others had 10 cm as the length of the hypotenuse. Some students had chosen to draw isosceles triangles; other students drew scalene triangles.

This task can be made more simple by asking students to draw accurate triangles and measure the sides. Then they can extend this to checking using Pythagoras’ theorem.

On the other hand, this task can be extended by asking students to generalise what they have found. If 10 cm is length of the hypotenuse, what can be said about the other two sides? If the triangle is isosceles, there is only one answer. But if it is scalene, perhaps students will call the length of the second side x. Then they can come up with a formula for the third side in terms of x. And how does this change if 10 cm is not the length of the hypotenuse but of one of the other sides?

The Plenary Pyramid

While teaching my year 8 class yesterday I used the last ten minutes on this plenary activity. Our lesson starter asked them to draw lines from their equations (for example, y = 2x + 3), and I managed to draw out some ideas about perpendicular lines and reciprocals. Then in the main part of our lesson we were working on a Maths Trail concerning systematic working. Students had to use a logical system to draw as many reflection patterns as they could, following a set of restrictions.

Here are some responses from the Plenary Pyramid.

I was surprised that:

There were so many possible reflection patterns.
Working systematically makes my head hurt.
Multiplying two reciprocals always gives the same answer.
Reciprocals are cool!
There were less than 100 but more than 50 [reflection patterns].

Questions:

What makes reciprocals so important?
How many reflection patterns are there?
How do we know for certain?
How much time would it take?
When are reciprocals used other than straight lines?
How to know the equation of a line.
Who made up the idea of perpendicular lines?

I learned:

What perpendicular means.
What systematically means.
That a rotated triangle does not count as a separate shape.
Shade triangles in a smart way.

This little activity for the end of a lesson helps me discover what went well and the students get to reflect on how successful they were. It lets me praise students for all they have learned. And I love it when students come up with interesting questions; it shows they are thinking mathematically.

What methods do you use to get feedback from students?