PrBL

= MATHEMATICS

SIMON BORGERT
HEAD TEACHER MATHEMATICS
KILLARA HIGH SCHOOL

@simonborgert
Simon.Borgert5@det.nsw.edu....
Liquorice Factory
Disclaimer: Not mine but from RIME
Everything was going along fine until one day
the Number 6 machine broke down!
No worries - just put the liquorice through ...
Liquorice Factory

In these times of hardship how many machines
do we really need? And what are they?	

Those who have the...
OR….
FUN WITH FACTORS
- EX 1.56 FROM
YOUR TEXTBOOK!
TRADITIONAL MATHEMATICS
CLASSROOM

Lesson

Bunch of Questions

Summative Assessment
PROBLEM BASED
CLASSROOM

Problem

Scaffolding

Summative Assessment
Pose the Problem

Knows
Need to knows
Next steps

Work on the problem
Intervention
Scaffolding

Move around
exemplar ideas...
Group 4 Solve
x+y=5

⎫
⎬
2
2
x + y = 13⎭

y = x − 3⎫
⎬
xy = 10 ⎭

y = 2x − 2

⎫
⎬
2
y = x − x − 2⎭

x − y = 1⎫
⎬
xy = 2 ⎭
...
Old Pedagogy

i
r

m
lu
u
c

r
u
C
n 2014
a
li
a
r
t
s
21st Century
u
A
Learner
NSW SYLLABUS

for the Australian
Curriculum
≠
RHS =

killarahighmaths
Google Drive
SEEMS TO BE WORKING……
THANKS
Voic ed presentationPrBl
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Presentation to VoicEd 2014 on Problem Based Learning and Mathematics

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  • Each machine takes our ‘base unit’ piece of liquorice and stretches it to the desired length - so put it in the 33 machine get a 33 piece
  • Have a go!
  • The alternative is a lecture style presentation on factors, multiples composite numbers primes etc followed by a textbook exercise
  • Teach the content - direct instruction - lecture style - 5 examples that cover all possible permutations of the questions
    Then a bunch of questions to practice the skills - problems
    followed by a summative assessment
    If we want our kids to creative problem solvers then why are we giving them the recipe before challenging them with problems - when does this ever happen in real life? -Factory model!
    When have you ever (in real life) had to solve a problem just after being taught the skills required to solve the problem
  • Front load the problem - back load the learning -a real ‘flip’ of the classroom
    Much more realistic
    Encourages creative thinkers
    Relate story - most intense mathematical situation I have ever been in - pager going off - back of pumper making calculations!
  • Pose the problem - can be linked to real life - can be straight pure mathematical!
    - knows - need to knows - next steps - a good idea to anticipate what the students will need to know - what the desired need to knows are and what questions you will ask to facilitate the desired need to knows!
    Next steps - problem solving strategies! - Act it out, look for a pattern, make a systematic list, guess and check, simplify the problems etc. - must be student generated- students need ownership of the learning
    Work on the problems - the student questions are where the learning is taking place - students must be actively struggling with the problem
    Solution - debrief is vital - what links to previous - what strategies worked/didn’t work- exit ticket - assessment: Posit it notes - A lightbulb moment, don’t forget, Improved, something you still have a question about
  • Problem to be solved can be purely mathematical - but without the spoon feeding before hand
  • The New Curriculum was an opportunity - and something to blame!
  • To change the perspective that the textbook is the bible and that we should be designing ‘learning activities”
  • •Set Up of [email_address] - Google Drive account
    oNot waiting for rollout across DEC
    oWill be easy to transfer to Google Apps in DEC – hopefully!
    oAll staff created their own gmail acouunt (If they didn’t have one)
    oA structural outline created
    oStaff are linking activities - rich tasks and problems directly to curriculum content
  • probably helps that I made a key component of registration being contributing to the collaborative program
    but teachers still want the textbooks….. - need to find a balance
  • Voic ed presentationPrBl

    1. 1. PrBL = MATHEMATICS SIMON BORGERT HEAD TEACHER MATHEMATICS KILLARA HIGH SCHOOL @simonborgert Simon.Borgert5@det.nsw.edu.au
    2. 2. Liquorice Factory Disclaimer: Not mine but from RIME
    3. 3. Everything was going along fine until one day the Number 6 machine broke down! No worries - just put the liquorice through the Number 2 Machine and then the Number 3 machine.
    4. 4. Liquorice Factory In these times of hardship how many machines do we really need? And what are they? Those who have the most efficient factory stay employed!
    5. 5. OR…. FUN WITH FACTORS - EX 1.56 FROM YOUR TEXTBOOK!
    6. 6. TRADITIONAL MATHEMATICS CLASSROOM Lesson Bunch of Questions Summative Assessment
    7. 7. PROBLEM BASED CLASSROOM Problem Scaffolding Summative Assessment
    8. 8. Pose the Problem Knows Need to knows Next steps Work on the problem Intervention Scaffolding Move around exemplar ideas clarifying questions Obtain a solution debrief process link to previous content?
    9. 9. Group 4 Solve x+y=5 ⎫ ⎬ 2 2 x + y = 13⎭ y = x − 3⎫ ⎬ xy = 10 ⎭ y = 2x − 2 ⎫ ⎬ 2 y = x − x − 2⎭ x − y = 1⎫ ⎬ xy = 2 ⎭ y = 2x − 5 −x − 5y + z = 17 ⎫ ⎪ −5x − 5y + 5z = 5 ⎬ 2x + 5y − 3z = −10 ⎪ ⎭ ⎫ ⎬ 2 y = x − 4x + 4 ⎭
    10. 10. Old Pedagogy i r m lu u c r u C n 2014 a li a r t s 21st Century u A Learner
    11. 11. NSW SYLLABUS for the Australian Curriculum
    12. 12. ≠ RHS = killarahighmaths Google Drive
    13. 13. SEEMS TO BE WORKING……
    14. 14. THANKS

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