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Planning for learning and teaching
"One of the teaching approaches which contribute particularly well to successful learning in mathematics is - well planned opportunities for children and young people to learn through investigate, active approaches" Learning Together: Mathematics - HMIE
The following questions may provide a stimulus for discussion:
- When planning learning and teaching what type of activities provide opportunities for learners to work independently as well as collaboratively?
- What steps are planned to review, improve and sustain these types of activities? See: Skills in Practice - Developing Thinking Skills
Well planned activities, incorporating Bloom’s Revised Taxonomy for Learning, are a useful tool for developing learners’ understanding and skills in numeracy and mathematics. The following activities have been developed to support staff to adopt the use of Bloom’s Revised Taxonomy in their planning:
- Bloom’s Revised Taxonomy planning tool for numeracy and mathematics can be used to support quality questioning.
- Bloom’s Higher Order Fans provide: Plenary questions to promote higher order thinking in the numeracy and mathematics classroom; exemplar activities which can be used to develop higher order thinking in numeracy and mathematics from early to fourth level in number and number process, fractions, decimal fractions and percentages and measurement.
Activities to support learning and teaching
This section is designed to support staff and learners by providing practical activities for the numeracy and mathematics classroom:
Practical activity 1 - Hinge questions
The Mathematics Excellence Group advocates strongly the planning of questions into lesson preparation. Such questions have been called 'hinge questions'. The idea is that the teacher plans every lesson with a 'hinge'; a point in the lesson when the teacher can check on student understanding, and then decide what to do next. 'Hinge' questions are typically designed to test learners' understanding of one important concept in a lesson—one that is critical for pupils to comprehend before the teacher moves on in the lesson.
Practical activity 2 - Starter and stand-alone activities
Putting a different ‘spin’ on lesson starters is one way to stimulate thinking and problem solving and also generates some very interesting discussions between learners and staff. Longer starters could be used as stand-alone activities during lessons.
Practical activity 3 - Self and peer assessment
Peer assessment makes greater demands on dialogue between learners. It encourages learners to externalise their thinking, explaining their understanding to others. In endeavouring to support others in their understanding, the learner is involved in utilising higher order thinking skills.
Practical activity 4 - Using incorrect answers
Through their use of effective questioning and discussion, teachers will use misconceptions and wrong answers as opportunities to improve and deepen children’s understanding of mathematical concepts.
Practical activity 5 - Using summative assessment formatively
Using summative assessments in a meaningful way to raise learners’ awareness of their strengths and development needs is vital in promoting understanding in mathematics. High quality discussion and debate from analysing summative tests provides an opportunity for learners to further develop higher order thinking and questioning skills.
- What kind of techniques and activities do you find are useful and effective for evaluating learners' progress informally?
- What kind of opportunities do you already provide for learners to discuss their progress?
About the author(s)
This resource was created within Education Scotland’s Numeracy team in conjunction with Scottish Government.