To develop higher-order thinking skills (HOTS) the mind needs to engage in higher-order learning task (HOLT). A good task for developing higher-order thinking skills is a problem solving task. But not all problems are created equal. Some problems are best suited for evaluating learning while others are best suited for assessing learning that would inform teaching. This post is about the second set of problems.The difference between these two sets of problems is not the content and skills needed to solve them but the way they are constructed.What are the features of a good problem solving task for learning mathematics?

- It uses contexts familiar to the students
- What is problematic is the mathematics rather than the aspect of the situation
- It encourages students to use intuitive solutions as well as knowledge and skills they already possess
- The task can have several solutions
- It challenges students to use the strategy that would highlight the depth of their understanding of the concept involved
- It allows students to show the connections they have made between the concepts they have learned

It is this kind of problem solving task that is used in the strategy Teaching *through* Problem Solving (T*t*PS) which I described in the previous post. Here is a sample task:

Students solutions to the task can be used to teach area of polygons, kinds of polygons, preserving area, and meaning of algebraic expression. You can use the task to facilitate students construction of knowledge about adding, subtracting, multiplying and dividing algebraic expressions. Yes, you read it right. This is a good problem solving task for introducing operations with algebraic expression through problem solving! The problem above is also an example of a mathematical tasks that links algebra and geometry. **Good mathematics teaching always links concepts.**

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