This week I will teach a lesson about estimating to my year 9s. The lesson will be a pretty standard one for me: a sequence of tasks and activities, some whole class items but mostly pair work. The lesson will involve some discussion about how and why someone might estimate the answer to a calculation. I’ll be using a few slides, a puzzle, some problems to solve (sourced from UKMT Intermediate contests), and a plenary about a poor guy whose calculator doesn’t display decimal points in answers.
But it’s the homework I want to talk about here. I plan to set a two part homework: read, then write.
1. Read
First students will read an article from earlier this year about two skiers who allegedly tied for first at the Sochi Olympics. Actually, their downhill skiing times were reported as identical due to rounding to two decimal places.
Two skiers tied for first (image: New York Times).
2. Write
Next, students will access a Google form that asks them three questions for which they need to write at least 300 characters (about 3 sentences). Here’s a copy of the form that you are welcome to answer “for fun”. (My students will be using a private version of this.)
I’m excited to see what students write in response to the third question: other examples (outside sport) where rounding of a measurement makes a crucial difference.
I’m interested to see what my students think about being asked to read and write for their maths homework. After reviewing literature and reflecting on my practice last school year, I decided to try a whole range of different homework options this year.
Our school offers the IB diploma for the final two years of secondary school. The maths courses each contain a 20% internal assessment that is a written report. So part of my interest in reading and writing in maths is to prepare students better for writing in maths during the IB diploma.
Have you tried out reading and writing activities in mathematics classes? Please tell me about it in the comments.
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.
read or outline a chapter (pre-learning)
complete an organizer of a chapter (pre-learning)
write down questions they have about a reading/activity
write/diagram all you know about [upcoming topic]
do a few sample questions and explain the steps
do practice questions (time-based)
answer journal questions about something done in class (ask students what was done and why)
two parts: 1. three problems to check understanding of a concept taught today; 2. ten problems to practice a concept previously learned
draw pictures/diagrams to illustrate a key word
create a concept map
write two problems for others to solve
list the four most important ideas about ….
read and write sticky notes for things you have questions about
design your own learning strategy for a topic covered in class (cards, song, poem, etc)
create a Q&A game
write directions that teach someone else
test corrections: must write why they missed that question, then answer the question correctly
find examples of … at home, in the news, etc; take pictures of … ; then use these in the next class
respond to a thread on Edmodo/other VLE asking a question or sharing an idea
“sandwich” homework: give students the problem and answer and they must fill in the middle
write a summary of today’s class
write a reflection of your work in today’s class
in class, do a notice/wonder activity and generate questions, then students pick one/two to investigate for homework
a project that shows your understanding
adaptive online software such as Khan Academy or MathXL
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)
Things to do with homework in class instead of collecting or checking it:
self-assess your homework in terms of effort, understanding, completeness, or accuracy
reflect on which questions were the easiest/hardest and why
find a peer who approached the problem differently than you and discuss our strategies
quiz with 2 randomly selected questions from the homework assignment
get your peer’s feedback on some aspect of your homework
work with a friend to get a best answer to one hard question
give a new problem and ask how it compares to the homework problem(s)
choose the two homework questions that were most alike or most different and explain why you picked them
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:
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.
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.
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.
