1. Active Learning in Mathematics

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

3. 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.

4. 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.

5. Current Views
Group formation
Activity 1 Card Sort Belief statements

6. 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

8. 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.

13. Some Principals that Support Active Learning
Teaching is more effective when it…
uses higher-order questioning
Activity 4: Dylan Williams – multiple answer questions
mins
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.

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

15. 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

18. 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.

20. 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.

21. 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.

24. 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.

25. Same Different
0.5
50% ⅝

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

27. Some Principals that Support Active Learning
Teaching is more effective when it…
Uses technology
Activity 10: Median and quartiles
Subtangent
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.

28. More Ideas!
Using Posters

29. Activity 11: Pair Posters

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

31. 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.

32. 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.

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

34. See more at:
and join!

35. 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