Challenging students to think critically

Teach Like a Champion Ch 9: Challenging students to think critically

  • Questioning can serve at least five purposes:
    • To guide students towards understanding new material
    • To push students to do a greater share of the thinking
    • To remediate an error
    • To stretch students
    • To check for understanding
    • Rules of thumb for designing effective questions:
      • One at a time
      • Simple to complex
      • Verbatim (don’t bait and switch): don’t change the question as a student is about to answer.
      • Clear and concise:
        • start with a question word
        • limit them to two clauses
        • write them in advance when they matter
        • ask an actual question
        • assume the answer is known i.e. ‘who can tell me’ not ‘can anyone tell me…?’
  • Stock questions: have similar sequences of questions that you apply over and over again in different settings.
  • Hit rate: should be above two-thirds but rarely 100%

Stretch It

Teach Like a Champion Technique 3: Stretch It.

The sequence of learning does not end with a right answer; reward right answers with follow-up questions that extend knowledge and test for reliability of knowledge. This technique is especially important for differentiating instruction.

  • Ask how or why.
  • Ask for another way to answer.
  • Ask for a better word.
  • Ask for evidence.
  • Ask students to integrate a related skill.
  • Ask students to apply the same skill in a new setting.

Teaching Mathematics Ch 5: Learning mathematics

  • Piaget argues that learning consists primarily in being faced with experiences that do not fit into our current understanding, meaning that such understanding needs to be adjusted (constructivism).
    • By implication, the teacher’s role is to discover pupils’ current levels of understanding, and offer learning experiences that challenge that understanding.
    • This will encourage pupils to develop new theories, and the teacher’s role is then to prompt pupils to test and refine those theories to reduce errors.
  • Social constructivism (e.g. Vygotsky) takes this theory further, arguing that effective learning can only take place in a social context.
    • By implication, mathematical discussion is much more important than transmission of knowledge from the teacher to the pupils.
    • The teacher’s role is to provide the scaffolding on which pupils construct their learning, by providing an appropriate level of challenge to each pupil.
  • Drawing this together, the teacher should: make the purpose of the lesson clear; build non-threatening relationships and environments; select challenging activities; intervene to help pupils develop their understanding of key ideas.
  • Possible lesson format based on constructivist approach:

Presentation – Exploration – Reflection – Consolidation

  • Another implication of the social constructivist approach is the value of group work, and particularly posing problems that generate disagreement and thus discussion amongst pupils.
  • Most misconceptions arise from over-generalisation of earlier mathematical learning.
    • Simply explaining that a method is wrong and showing the correct method often isn’t enough to address the misconception.
    • Instead the teacher needs to create uncertainty in the pupils through cognitive conflict, and be brave in doing so!
    • This can be achieved through designing activities that will encourage misconceptions to come to light by pupils getting two contradictory answers.
  • Swan discusses this model in five steps:
  1. Assess pupils’ initial understanding

  2. Pupils complete a task that exposes misconceptions and causes cognitive conflict.

  3. Pupils share their methods and solutions through discussion.

  4. The teacher organises whole-class discussion to resolve conflict.

  5. Pupils consolidate learning through applying it to new problems.

  • Activities that suit this type of teaching include sorting activities, and always, sometimes, never, classifying into two-way tables, pupils making up questions, pupils marking answers to questions.

A great series of problem-solving lessons on Pythagoras

Problem-solving lessons on Pythag

This article offers good insights into how to design a series of interlinked lessons and homework tasks in order to teach Pythagoras’ theorem in a problem-solving approach. It contains good AfL, lots of group work and carefully thought-through homework.

I can refer back to this when seeking to design a series of lessons on another topic.

The Lazy Teacher’s Handbook: Ch 8 Differentiation

Three golden rules:

  • Differentiate for all through variety in your lessons over the term
  • Ask others (professionals, learners) what differentiation they feel is needed
  • Make differentiated strategies clear to the class so that they can differentiate for themselves.


Ways to differentiate the classroom experience:

  • Have plants that the students look after
  • Cultivate wonder through having weird props (regularly changed)

[These are great ideas but they aren’t differentiation as I understand it]


Ways to differentiate tasks:

  • Get students to design the task
  • Share Bloom’s Taxonomy with the class and make clear that you will be asking questions at different levels.
  • Have low access-high challenge tasks, and open questions
  • Get students to start the challenge just before it is getting difficult for them.
  • Make it clear where students can find help other than from you.
  • Matching learners
  • Ask learners what they need to learn better
  • Get a panel of students to review your intended tasks for the forthcoming lessons, suggest amendments and then surprise them by asking them to teach it.
  • Allow students to produce work in a variety of formats
  • Model how the task might look at different stages (perhaps by asking another group to do so?)
  • Think about what can be recorded that the students can refer back to.
  • Use what you know about the class.
  • Have high expectations of everyone.