Continuous Professional Development in Mathematics What are Higher

Continuous Professional Development in Mathematics What are Higher Order Thinking Skills?

What are higher order skills? Higher Order Skills Higher order skills are skills involving analysis, evaluation and synthesis (creation of new knowledge). These are thought to be of a ‘higher order’, requiring different learning and teaching methods than the learning of facts and concepts. Higher Order Thinking Higher order thinking involves the learning of complex judgmental skills such as critical thinking and problem solving. Higher order thinking is more difficult to learn or teach but also more valuable because such skills are more likely to be usable in new and unfamiliar situations. Higher Order Questioning Higher order questions require answers that go beyond simple information and as such both the language and thinking behind them is more complex. They take learners into abstract language functions, such as giving and justifying opinions, speculation and hypothesising. Are you already doing some of these?

In practice: Problem solving using Higher Order Skills To set the scene, watch this clip on a classroom practitioner talking about how to create more independent problem solvers. [ Dan Meyer: Math class needs a makeover ] Video clip on TED Talks website

The backbone for all of this is Bloom’s Taxonomy…

BLOOM’S TAXONOMY Creating Generating new ideas, products, or ways of viewing things Designing, constructing, planning, producing, inventing. Evaluating Justifying a decision or course of action Checking, hypothesising, critiquing, experimenting, judging Analysing Breaking information into parts to explore understandings and relationships Comparing, organising, deconstructing, interrogating, finding Applying Using information in another familiar situation Implementing, carrying out, using, executing Understanding Explaining ideas or concepts Interpreting, summarising, paraphrasing, classifying, explaining Remembering Recalling information Recognising, listing, describing, retrieving, naming, finding Hig thi he nk r o ing rde ski (HO r lls T)

BLOOM’S TAXONOMY Creating Generating new ideas, products, or ways of viewing things Designing, constructing, planning, producing, inventing. Evaluating Justifying a decision or course of action Checking, hypothesising, critiquing, experimenting, judging Analysing Breaking information into parts to explore understandings and relationships Comparing, organising, deconstructing, interrogating, finding Applying Using information in another familiar situation Implementing, carrying out, using, executing Understanding Explaining ideas or concepts Interpreting, summarising, paraphrasing, classifying, explaining Remembering Recalling information Recognising, listing, describing, retrieving, naming, finding Using knowledge of fractions, write a question given a context/problem. Hig thi he n. Inkcontext, r ocompare rde of ingwith a variety fractions (H r different ski denominators and come decision. lls to a O T) Given a fraction of a quantity, find the total amount. Find the fractions of a quantity. Order the fractions you know. List all the fractions you know.

How do I know what knowledge and skills to involve in my planning? Topic: 3 D Shape E&O: MTH 2 -16 a E& O Knowledge: 1. Range of 3 D objects 2. Their properties Skills: 1. 2. 3. 4. 5. Explored Use mathematical language Describe Investigation Discuss where and why particular shapes are used in the environment Having explored a range of 3 D objects and 2 D shapes, I can use mathematical language to describe their properties, and through investigation can discuss where and why particular shapes are used in the environment. MTH 2 -16 a Practice: 1. 2. 3. 4. 5. 6. 7. Effective Questioning 1. Discussion Use misconceptions Use wrong answers Relevant contexts Experiences familiar to young 2. 3. people Solve problems Principles and Practice 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 using relevant contexts and experiences, familiar to young people Mathematics is at its most powerful when the knowledge and understanding that have been developed are used to solve problems

How do I know what knowledge and skills to involve in my planning? Topic: 3 D Shape E&O: MTH 2 -16 a Knowledge: 1. Range of 3 D objects 2. Their properties Planning using Bloom’s Taxonomy ailed s Det Grid m’ Bloo Skills: 1. 2. 3. 4. 5. Explored Use mathematical language Describe Investigation Discuss where and why particular shapes are used in the environment Practice: 1. 2. 3. 4. 5. 6. 7. Effective Questioning Discussion Use misconceptions Use wrong answers Relevant contexts Experiences familiar to young people Solve problems Bloom’s Mini Grid ’s Bloom Fan Exemplars and guides on these three tools are provided in this pack

Activity 1: Using the mini grids ‘Bloom’s mini grid’ 1. Look through three of the sample mini grids provided • Look at the differences between the LOT and the HOT skills 2. In group(s) complete a grid for a topic using the blank grids provided.

Taking it further… Using the detailed grids We can take these handy ‘mini’ grids a bit further and use more detailed grids ( shown below) as a CPD activity to support understanding and use of Higher Order Skills in the maths learning environment.

Activity 2: Using the detailed Grids Part 1 In a group(s), have a look through the exemplar detailed grids supplied in this pack. Discuss: • When you use similar Higher Order Skills (top 3 rows) in your classroom • The benefits of using these higher order approaches with pupils • Other topics these skills and approaches could transfer too • Ideas you could use immediately in your classroom

Activity 2 Part 2 • In a group(s), decide on a topic to focus on. • Using the E&O(s) and Principles and Practice paper decide on the knowledge, skills and practice that will be involved • Complete a blank grid for this topic • Can you add a few more keywords? • Create questions/questioning approaches for each level • Share your grid with other groups Reflection • Why are higher order skills (the upper three rows) so beneficial in the classroom? • Individually, share how you plan to incorporate some of these higher order skills into your classroom…immediately? Over the longer term?

Further materials supplied in this pack In this pack This pack includes materials to increase focus on Higher Order Skills that can be used: 1. By a department as CPD 2. By a teacher in their classroom 3. By pupils in the course of their learning Be creative with the materials as they can be used in a multitude of ways. Feel free to edit, amend, change and improve materials to best suit your learners.

Brief overview of whole resource This Powe CPD Session r. Point! Overview of H. O. S. Scene setting Summary of attached materials (EG) and Teaching Planning Learning using Bloom’s 1. Detailed grids + CPD 2. Mini grids + CPD 3. Fans + CPD (stand-alone) Learning and Teaching - Everyday strategies Hinge Questions +CPD Self and peer assessment +CPD Using wrong answers +CPD Starter/Stand alone activities +CPD Using summative formatively +CPD

Further materials supplied in this pack Planning using Bloom’s Taxonomy m’s D Bloo d. G etaile rid Bloom’s Mini Grid s Fan ’ Bloom Learning and Teaching – Everyday strategies Hinge Questions Starters and Stand Alone Activities Self & Peer Assessment Think-Pair -Share Using wrong answers Beat the Class Foldy Making Summative Formative