Active Learning in Mathematics

Task During this session we will review what ‘active maths’ is, along with a dozen activities that support active learning.

Learning intentions Understand the difference between passive and active learning. To try a range of activities and link these with some of the key principals of active learning.

Success Criteria I have examined my own beliefs about maths learning. I have understood the concept of ‘active learning’. I have participated in the learning activities and considered how I could incorporate these or similar activities in my teaching.

Current Views Group formation Activity 1 Card Sort Belief statements

From ‘Passive’ to ‘Active’ Learning “I listen while the teacher explains.” “I copy down the method from the board or textbook.” “I only do questions I am told to do.” “I work on my own.” “I try to follow all the steps of a lesson.” “I do easy problems first to increase my confidence.” “I copy out questions before doing them.” “I practise the same method repeatedly on many questions.” “In many of the mathematics lessons where learning is unsatisfactory one or more of the following characteristics are evident: students are given low-level tasks which are mechanistic and can be completed by imitating a routine or procedure without any depth of thought students are mainly receivers of information, and have little opportunity for more direct participation in the lesson and the exploration of different approaches insufficient time is allowed for students to develop their understanding of the mathematical concepts being taught students have too little time to explain their reasoning and consider the merits of alternative approaches.” [16]2

Some Principals that Support Active Learning Teaching is more effective when it… builds on the knowledge learners already have. exposes and discusses common misconceptions. Activity 2: Time Activity 3: Exam questions Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Some Principals that Support Active Learning Teaching is more effective when it… uses higher-order questioning Activity 4: Dylan Williams – multiple answer questions http://www.ltscotland.org.uk/numeracy/aboutnumeracy/numeracyconference09.asp 26 - 32mins Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Questioning in maths: diagnosis In which of these right-angled triangles is a2 + b2 = c2 ? A a c b C E B D F

Eliciting evidence Key idea: questioning should cause thinking provide data that informs teaching Improving teacher questioning generating questions with colleagues closed v open low-order v high-order appropriate wait-time Getting away from I-R-E basketball rather than serial table-tennis ‘No hands up’ (except to ask a question) class polls to review current attitudes towards an issue ‘Hot Seat’ questioning All-student response systems ABCD cards, Mini white-boards, Exit passes

Some Principals that Support Active Learning Teaching is more effective when it… uses cooperative small group work Activity 5: Team game Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Some Principals that Support Active Learning Teaching is more effective when it… Encourages reasoning rather than ‘answer getting’ Activity 6: Sometimes / always / never Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Some Principals that Support Active Learning Teaching is more effective when it… uses rich collaborative tasks Activity 7: Jigsaws Activity 8: Using mark schemes Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Some Principals that Support Active Learning Teaching is more effective when it… creates connections between topics Activity 9: Fractions decimals percentages washing line from Peter Patilla human number line Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

Same Different ½ 0.5 50% ⅝ 0.500000

Making connections: The three-times table Multiples of 3 Input x3 output x 3x Y = 3x

Some Principals that Support Active Learning Teaching is more effective when it… Uses technology Activity 10: Median and quartiles Subtangent http://www.subtangent.com/maths/median-and-quartiles.php Effective teaching assumes that learners do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning to adapt to the needs of learners [9]. This prior learning may be uncovered through any activity that offers learners opportunities to express their understanding. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to set the agenda for that session and elicit a range of explanations. These responses may then be used as a starting point for discussion.

More Ideas! Using Posters

Activity 11: Pair Posters

More Ideas Active activities that require learners to move! Activity 12: Treasure hunt and Talking chips

Learning intentions Understand the difference between passive and active learning. To try a range of activities and link these with some of the key principals of active learning.

Success Criteria I have examined my own beliefs about maths learning. I have understood the concept of ‘active learning’. I have participated in the learning activities and considered how I could incorporate these or similar activities in my teaching.

Reflection Take some time to consider what we have covered today and try to identify the next steps you would like to take.

See more at: http://moray-literacy-and-numeracy.wikispaces.com/ and join!

Reading & References “Building Learning in Mathematics” Prestage, Watson & De Geest “Mathematical Treasure-Hunts” Lucas “Interactive Mental Maths” Patilla “Thinking Through Mathematics” NRDC Dylan Williams keynote speech at National Numeracy Conference 2009 http://www.ltscotland.org.uk/numeracy/aboutnumeracy/numeracyconference09.asp