reading/learning – Page 3 – In Pursuit of Great Mathematics Teaching

Better Group Work

I just finished reading an article called “When Smart Groups Fail” (Barron, 2003). It’s a study of groups of three sixth graders solving maths problems. Barron divides the groups into less successful and more successful at solving the problems and then analyses what features of their group work were significant.

Surprisingly to me, the success of a group of students was not influenced by:

the amount of talk
the average achievement level of the students
whether anyone in the group had a correct idea

Instead, Barron found that group success was marked by:

accepting or discussing correct ideas rather than dismissing them
correct ideas were brought up when they related to ideas that were being discussed at the moment
group members paid attention to each other and if the others were paying attention to them
group members physically showed their togetherness by eye contact and standing around or pointing to a common workbook

This article’s findings indicate to me that my classroom culture can lead to better group work. I can help students learn to discuss a mathematical idea by building on each other’s thoughts. A well-managed whole group discussion can lead to more cooperative group work sessions. I want my students to learn to listen carefully to what is said and then agree or disagree or ask questions. I can request these responses in whole class time. Then students will see they are the norms that also should guide their group work.

Furthermore, the groups in Barron’s study were of mixed ability and their previous achievement levels did not correlate with their success as a group. This adds to my feelings about the benefits of mixed ability teaching. If students of differing abilities can be helped to communicate well, they can all achieve well.

The study also found that students in successful group went on to be more successful in individual tasks. Interestingly, students in less successful groups did as well as if they had worked on their own. Thus poor group work neither helped nor hindered their achievement. However, good group work improved the success of individual students in to a significant degree.

The school year is just about to start and I am looking forward to inculcating a culture of social, mathematically focused talk.

Barron, Brigid. “When Smart Groups Fail.” The Journal of Learning Sciences 12.3 (2003): 307-359.

Vital Behaviours

It’s orientation week for new teachers at my school and the head of school gave a welcome talk. In it he mentioned vital behaviours for teachers and students for success at school. Afterwards I did a bit of reading about vital behaviours. (Here are two posts that helped me.) The phrase is from a book called Influencer: The New Science of Leading Change. Vital behaviours are those actions that lead to our goals. They are the smallest possible actions that make the biggest impact towards meeting goals.

Our head of school identified three vital behaviours for successful students:

attendance
completion of homework
leadership outside of the classroom

He also identified three vital behaviours for successful teaching staff at our school:

collaboration
use of data and evidence to guide decisions
high expectations for all students

The idea of vital behaviours really stuck with me. And made me wonder if I can generate some of my own. First I would need to think of a goal and then identify the fewest essential actions to meet that goal.

And since it’s goal setting time for the new school year, I thought I would give it a try.

Goal: Coach my grade 9 students (two classes) to communicate meaningfully in their maths portfolios/journals. (I’m not sure yet what I am going to call these books.)

First I brainstormed the steps I might take to work towards this goal.
introduce journals
provide exemplars (I already have some pictures of these.)
examine with students: What is meaningful communication and reflection?
establish thinking routines
provide rich tasks
provide reflection time
give summative feedback on tasks
have students give regular presentations in front of class
peer assess communication
write a rubric of expectations

And then I refined these to a list of vital behaviours:

provide rich tasks
provide reflection time
examine with students: what is meaningful communication and reflection?

I’m sure that after school actually starts I will see if this goal and these behaviours need to be updated or changed.

Have you ever used the idea of vital behaviours in your planning?

What are your goals for this school year?

Maths Trauma

Over the next three weeks, I’m participating in a free online course called How to Learn Math. It’s offered by Jo Boaler from Stanford University. I recently read Boaler’s book The Elephant in the Classroom (published in the USA with the title What’s Math Got to Do With It?). The course consists of short (5 minute) video segments, interspersed with tasks for me to do.

One of today’s tasks was to watch a short video of university students who describe difficulties they had with school mathematics. This concept map (below) summarises their perceptions of maths.

Similarly, a lot of adults talk about the trauma they experienced at school related to maths. As I meet people and tell them I’m a maths teacher, the usual response by adults of all backgrounds and careers is “I was so bad at maths.” A lot of highly successful adults hated maths at school and still think they are bad at it.

I have become very concerned with the way parents talk about their lack of maths ability in front of their children. For example, on parents’ evening I often hear a parent say, “I can’t help her with her maths homework at all. I am so bad at maths.” I think this is a very irresponsible thing for a parent to say. It doesn’t help the child see that maths is something at which they can improve. I am still looking for a tactful and helpful reply to these adults!

Was maths traumatic at school for you?

How would you reply to an adult who was traumatized by maths?

Teaching to the Test

While reading today, I discovered an unexpected side effect of the practise of teaching to the test. (At least it was unexpected to me; perhaps you will not find it so surprising?)

First, the “usual” problems with extended coaching[1] for exams:

the exam is no longer a good indicator of what students understand since they have only been narrowly trained to do specific question types
the exam is no longer a useful way of selecting students for further courses since we don’t know if they really understood the mathematics they have “learned”
the possible ranking of schools (for example, league tables in the UK) by student grades is not accurate since some schools have used extensive coaching while others have not
employers can not be sure that students’ ability matches their test score

All these arguments are ones I have heard before about coaching students to pass an exam. But one undesirable side effect of exam coaching stood out to me:

younger children see older ones being coached to success and they learn that at just they right time, they, too, will be spoon-fed what they need to know

As a result students learn that they do not need to take responsibility for their own learning, they do not need to study seriously or make an effort to understand and connect what they are learning.

Wow! I was shocked by this. One of my main goals is to make sure students understand what they are learning and can connect their mathematical ideas. I don’t want younger ones to learn that they don’t really need to work hard until the exam coaching begins.

My school only partly subscribes to the idea of coaching for exams. But I fully subscribe to the idea that students need to take responsibility for their own learning.

What exam preparation strategies do you use?

[1] I am talking about the repetitious, algorithmic coaching that happens in the lead up to standardised tests. Students, especially those who are near a grade level borderline, are taken (forcibly, at times) though many, many revision resources.

Ken Robinson: Escaping Education’s Death Valley

I was watching this TED talk today in which Ken Robinson talks about the characteristics of successful education systems. He mentions three main things that are needed:

1. An understanding that education needs to be made up of individualised teaching and learning experiences, since all children are different

2. An investment in the best people as teachers and in their support and professional development

3. Authority for making educational decisions is devolved to the school level

Sir Robinson puts a lot of stress on the human aspect of education and rejects the idea that schools are an industrial machine for transferring knowledge. Instead, children’s curiosity needs to be nurtured. Teaching is an inherently creative job.

Leadership in education, therefore, at regional and school levels, needs to be focused on creating a climate of possibility.

In my current role (coordinator of IB DP maths), this means that I need to foster teachers’ creativity (and my own). As part of the maths leadership team I can encourage us all to teach more inquiry-based lessons, which is one of our goals this year. As I try new ideas myself I can share my experiences. And I have lots to learn from what the others around me are doing.

Procrastination

Late in the afternoons when the maths office is quiet, I like to set aside the emails, form-filling-in, reports, lesson planning, and admin jobs, and just do some reading for the pleasure of learning something. Sometimes I read about maths teaching theories. I like to read scholarly papers. Or I read an article from Mathematics Teaching (the ATM journal) or Mathematics in School (the MA journal). I also usually find lots of ideas for things to read from my Twitter feed.

Is my afternoon reading habit a form of procrastination? I choose to believe that it is not. It is more of a break for my brain and a chance to recharge. I always feel really refreshed by learning something new. I often pick up a new idea about how to teach a tricky topic. Quite often I read about productivity and gain a bit of motivation to work more efficiently and effectively. Recently I have been reading about leadership in connection with my Links course.

If I’m honest, sometimes I do procrastinate by reading. It’s a chance to avoid things I don’t like doing for a while. At least I get something good out of it at the same time.

Today I stumbled upon this article about 15 things that good leaders do automatically every day. One of them was that they don’t procrastinate! I was really struck by the idea that good leaders are proactive and keep their progress moving by not avoiding jobs, even unpleasant ones. Good leaders know that “getting ahead in life is about doing the things that most people don’t like doing.” I feel a renewed sense of purpose after reading that. I want to be the kind of person who approaches life with determination, from the most important jobs (planning for great lessons) to the most mundane (administrivia). I’m glad I took my late afternoon reading break to gain that sense of momentum again.

Do you procrastinate? Do you have any procrastination tips?

Classroom Decoration and Design

From this NY Times article, I learned that humans are more productive when they work in well designed, well decorated spaces. A study on people in hospitals, offices, and schools has shown that a window view with a landscape outside helps them be more productive and healthier. Also, humans like to look at fractals (and fractals of a certain density), and this helps them perform better, too.

The implications for teachers are clear.

1. Try to get a classroom with a view!

2. Decorate your classroom with shades of green and landscapes.

3. Put fractals up – not too sparse and not too dense.

Leadership Styles

I have been reading today about instructional leadership and transformational leadership. Here are the definitions I have uncovered so far.

Instructional leadership focuses on how the school leader engages with teaching and learning. A strong, directive leader becomes a culture builder in a school by communicating a mission. The leader talks over and over about the mission and it is embedded into classroom practice and policies. The leader also takes an active role in managing staff and the curriculum. They work directly on teaching and learning issues. They are highly visible and have high expectations. The instructional leader protects teaching time and promotes professional development.

Transformational leadership describes a process by which a leader increases support for common goals. They seek to improve staff and themselves. There is a collaborative culture in which all are encouraged to participate and grow.

According to the article I have been reading by Viviane Robinson (2007), instructional leadership has a much greater positive impact on student outcomes than transformational leadership.

I am aware that I am an emerging leader; I am still developing my style of leadership. I can see the impact that I could have as an instructional leader. It seems to me that I may be helped by developing some charisma, though! (Is that even possible?) I have worked under a headteacher who was a dynamic instructional leader; he was also so demanding that many staff felt burnt out. I think sometimes I tend to the collaborative structures of transformational leadership because I am conflict-averse. Seeking others’ opinions seems like a safe way to proceed since then I cannot displease anyone.

I have more to say and I need more time to think and write. But I need to get back to the business of planning lessons.

I think that planning lessons is my prime task as a teacher. One article I read today (also Viviane Robinson) said that educational leaders should focus more on leading teaching and learning. This gives me lots to (hopefully) think about and digest soon.

Swap and Spot the Error

Here is a strategy I use to get students thinking. My year 11s have learned some trigonometry recently and everyone is working at their own pace. Some are still doing basic trig and others are doing complex multistep problems with bearings or in 3D. I used this slide (revealing one sentence at a time) to run a starter activity.

First I encouraged them to make a problem that would challenge their partner (who is the person sitting next to them). Then their partner was told to answer the question, but make a mistake on purpose. Then a third person checks over the work and tries to spot the error.

Each student is engaged in this starter and no one sits passively. (I created it after reading Kagan’s Cooperative Learning book, which states that as many students as possibly should be active during an activity.) The problems the students made up were more interesting and many were more challenging than textbook or worksheet questions. And each student was exposed to three problems: the one they created, the one they solved, and the one they checked. My year 11s enjoyed the social aspect, too.

“Swap and Spot the Error” is a task that you can use for many topics. Try it and let me know how it goes.

Giving Options to Students

I have been reading More Good Questions by Marian Small. One differentiation strategy she recommends is to give students 2 options. The questions are related and the follow-up discussion engages students who did either option. For the question above, we talked together after a few minutes.

What is the area of each of the full circles in your picture?
How can you test that the answer is reasonable?

I set these cheese questions for some year 11 students who are revising for their IGCSE Foundation exam. After a few minutes we talked about the two answers using these questions.

Which measurements did you use?
Did you look up any formula?
What units did you use for your final answer?

These two questions are available here.