active learning in mathematics. task during this session we will review what ‘active maths’ is,...

TaskTask

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

Learning intentionsLearning intentions

Understand the Understand the difference between difference between passive and active passive and active learning.learning.

To try a range of To try a range of activities and link activities and link these with some of these with some of the key principals of the key principals of active learning.active learning.

Success CriteriaSuccess Criteria

I have examined my own beliefs about I have examined my own beliefs about maths learning.maths learning.

I have understood the concept of ‘active I have understood the concept of ‘active learning’.learning’.

I have participated in the learning activities I have participated in the learning activities and considered how I could incorporate and considered how I could incorporate these or similar activities in my teaching.these or similar activities in my teaching.

Current ViewsCurrent Views

Group formationGroup formation

Activity 1 Card Sort Activity 1 Card Sort Belief statementsBelief statements

From ‘Passive’ to ‘Active’ LearningFrom ‘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.”

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more Teaching is more effective when it…effective when it…– builds on the builds on the

knowledge learners knowledge learners already have.already have.

– exposes and exposes and discusses common discusses common misconceptions.misconceptions.

Activity 2: TimeActivity 2: Time

Activity 3: Exam Activity 3: Exam questionsquestions

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more effective when it…Teaching is more effective when it…– uses higher-order questioninguses higher-order questioning

Activity 4: Dylan Williams – multiple answer Activity 4: Dylan Williams – multiple answer questionsquestions

http://www.ltscotland.org.uk/numeracy/aboutnuhttp://www.ltscotland.org.uk/numeracy/aboutnumeracy/numeracyconference09.aspmeracy/numeracyconference09.asp

26 - 32mins 26 - 32mins

Questioning in maths: diagnosisQuestioning in maths: diagnosisIn which of these right-angled triangles is aIn which of these right-angled triangles is a22 + b + b22 = c = c2 2 ??

A a

c

b

C b

c

a

E c

b

a

B a

b

c

D b

a

c

F c

a

b

Eliciting evidenceEliciting evidenceKey idea: questioning shouldKey idea: questioning should

– cause thinkingcause thinking– provide data that informs teachingprovide data that informs teaching

Improving teacher questioningImproving teacher questioning– generating questions with colleagues generating questions with colleagues – closed v openclosed v open– low-order v high-orderlow-order v high-order– appropriate wait-timeappropriate wait-time

Getting away from I-R-EGetting away from I-R-E– basketball rather than serial table-tennisbasketball rather than serial table-tennis– ‘‘No hands up’ (except to ask a question)No hands up’ (except to ask a question)– class polls to review current attitudes towards an issueclass polls to review current attitudes towards an issue– ‘‘Hot Seat’ questioningHot Seat’ questioning

All-student response systemsAll-student response systems– ABCD cards, Mini white-boards, Exit passesABCD cards, Mini white-boards, Exit passes

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more effective when it…Teaching is more effective when it…– uses cooperative small group workuses cooperative small group work

Activity 5: Team gameActivity 5: Team game

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more Teaching is more effective when it…effective when it…– Encourages reasoning Encourages reasoning

rather than ‘answer rather than ‘answer getting’getting’

Activity 6: Sometimes / Activity 6: Sometimes / always / neveralways / never

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more Teaching is more effective when it…effective when it…– uses rich collaborative uses rich collaborative

taskstasks

Activity 7: JigsawsActivity 7: Jigsaws

Activity 8: Using mark Activity 8: Using mark schemesschemes

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more Teaching is more effective when it…effective when it…– creates connections creates connections

between topicsbetween topics

Activity 9: Fractions Activity 9: Fractions decimals percentages decimals percentages washing line from washing line from Peter Patilla human Peter Patilla human number linenumber line

SameSame DifferentDifferent

½½0.50.550%50%⅝⅝0.5000000.500000

636363

Making connections:Making connections:The three-times tableThe three-times table

Multiples of 3Multiples of 3

Input Input x3x3 outputoutput

xx 3x3x

Y = 3xY = 3x

Some Principals that Support Some Principals that Support Active LearningActive Learning

Teaching is more effective when it…Teaching is more effective when it…– Uses technologyUses technology

Activity 10: Median and quartilesActivity 10: Median and quartiles

SubtangentSubtangent

http://www.subtangent.com/maths/median-and-http://www.subtangent.com/maths/median-and-quartiles.phpquartiles.php

More Ideas!More Ideas!Using PostersUsing Posters

Activity 11: Pair Posters

More IdeasMore Ideas

Active activities that require learners to Active activities that require learners to move!move!

Activity 12: Treasure hunt and Talking Activity 12: Treasure hunt and Talking chipschips

Learning intentionsLearning intentions

Understand the Understand the difference between difference between passive and active passive and active learning.learning.

To try a range of To try a range of activities and link activities and link these with some of these with some of the key principals of the key principals of active learning.active learning.

Success CriteriaSuccess Criteria

I have examined my own beliefs about I have examined my own beliefs about maths learning.maths learning.

I have understood the concept of ‘active I have understood the concept of ‘active learning’.learning’.

I have participated in the learning activities I have participated in the learning activities and considered how I could incorporate and considered how I could incorporate these or similar activities in my teaching.these or similar activities in my teaching.

ReflectionReflection

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

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

and join!and join!

Reading & ReferencesReading & References

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