I always put homework details online as well as explaining it in class. I use a blog (which doesn’t turn up in web searches) with a page for each class. I find publishing the details online for students makes me think about explaining it carefully and I can also give any links to resources which may help. None of my students can ever say to me that they didn’t know what the homework was!
Homework does not necessarily have to be on the topic you are currently studying and can offer the chance to review previous topics or look ahead to a topic you will be studying. Some alternatives to the textbook:
Set some questions with solutions and mark schemes
Students write questions on a given topic and also provide solutions and a mark scheme. In class their peers can try the questions. This offers the chance for some excellent class discussion on why students think a question is a good question, the difficulty of a question and how it should be marked.
Alternatively ask them to write some diagnostic questions with multiple choice answers. Ask them to provide the question with four possible answers. They should indicate which answer is correct and explain their reasoning behind the options they have given.
A variation on this idea is to ask students to choose something like a UK Maths Challenge question for the class. Full solutions to the UK Maths Challenge questions are available so a student or students could come to the lesson prepared to set the question for the class and provide feedback.
Give two fairly / very similar homeworks in a row, the second being a chance to act on all the fabulous feedback you gave for the first attempt!
Direct students to some resources to study a topic before you do this in class. The introduction to the topic can then explore and build on the ideas they have already. The class could be asked to write down any ideas they have / draw pictures on an A3 piece of paper in groups. This could also be used for a revision activity.
Whilst flipped learning is definitely not all about watching videos, they can be useful; any resources for students to study need to be very carefully chosen so they really are accessible to a student working at home. Clearly a teacher needs evidence that the work has been done – students can write down questions that arise from studying any resources, they should also come to class prepared to answer questions. I am not advocating that we all flip our classrooms – just that the ideas can be used for homework sometimes.
Revise and Recall
Help students recall material by setting a homework to review a topic or topics and then give a mini-test in class. I tend to call them ‘Self-checks’ for the students to emphasize the idea they are just checking what they know and what they may need further help with.
Nrich has already been mentioned, many of the other resources on the Rich Tasks page offer possible homework problems. For example see the AQA outstanding resource ‘Problem Solving Questions’ which includes numerous problems. The solutions document includes indices by topic and also by process.
(Direct links to the guide and solutions.)
Use Online Resources
Such as WolframAlpha or the Desmos graphing calculator.
For example, Further Mathematicians could be directed to explore families of polar curves – then identify which is which in class.
More on WolframAlpha.
Posts for students on the Desmos graphing calculator: Explore Straight Lines and Explore Graphs.
Dictionaries such as A Maths Dictionary for Kids by Jenny Eather or the Illustrated Mathematics Dictionary from Math is Fun can be used to give definitions of terms. Both of these dictionaries give clear definitions and provide examples, I often use an entry to define a term in class. Both of these dictionaries have been well received by students. The Math is Fun dictionary provides links to further information and provide activities for students to try. Dictionary exercises could be set for homework; see, for example, the Dictionary Exercises under Other Activities on the Cleave Books, Teacher Resources OnLine (trol) site (resources on the trol site were developed by the late Frank Tapson, a former long term employee of the Centre for Innovation in Mathematics Teaching in Plymouth.)
Let the students choose! See this page where I have included my suggestions for my classes who decided they like the idea of an independent homework.
Write a Mathematics journal entry.
Create a Wiki for your class and ask students to create pages. They could create a collaborative revision resource.