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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