Blake Institute June 2014 Day 1

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  • 1. Day 1 | June 2014 Singapore Mathematics Institute with Dr. Yeap Ban Har coursebook
  • 2. 2 | P a g e Contact Information  yeapbanhar@gmail.com  www.banhar.blogspot.com about yeap ban har Dr Yeap Ban Har spent ten years at Singapore's National Institute of Education training pre-service and in-service teachers and graduate students. Ban Har has authored dozens of textbooks, math readers and assorted titles for teachers. He has been a keynote speaker at international conferences, and is currently the Principal of a professional development institute for teachers based in Singapore. He is also Director of Curriculum and Professional Development at Pathlight School, a primary and secondary school in Singapore for students with autism. In the last month, he was a keynote speaker at World Bank’s READ Conference in St Petersburg, Russia where policy makers from eight countries met to discuss classroom assessment. He was also a visiting professor at Khon Kaen University, Thailand. He was also in Brunei to work with the Ministry of Education Brunei on a long-term project to provide comprehensive professional development for all teachers in the country.
  • 3. 3 | P a g e introduction The Singapore approach to teaching and learning mathematics was the result of trying to find a way to help Singapore students who were mostly not performing well in the 1970’s. The CPA Approach as well as the Spiral Approach are fundamental to teaching mathematics in Singapore schools. The national standards, called syllabus in Singapore, is designed based on Bruner’s idea of spiral curriculum. Textbooks are written based on and teachers are trained to use the CPA Approach, based on Bruner’s ideas of representations. “A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them”. | Bruner 1960 “I was struck by the fact that successful efforts to teach highly structured bodies of knowledge like mathematics, physical sciences, and even the field of history often took the form of metaphoric spiral in which at some simple level a set of ideas or operations were introduced in a rather intuitive way and, once mastered in that spirit, were then revisited and reconstrued in a more formal or operational way, then being connected with other knowledge, the mastery at this stage then being carried one step higher to a new level of formal or operational rigour and to a broader level of abstraction and comprehensiveness. The end stage of this process was eventual mastery of the connexity and structure of a large body of knowledge.” | Bruner 1975 Bruner's constructivist theory suggests it is effective when faced with new material to follow a progression from enactive to iconic to symbolic representation; this holds true even for adult learners. | Bruner 1966
  • 4. 4 | P a g e Early Numeracy |Session 1  Rational Counting  Number Bonds  Lesson Sequence  Use of Literature Lesson Sequence  Anchor Task  Guided Practice  (Independent Practice) Case Study 1 |  Show 5 beans on a ten frame.  Do it in another way.
  • 5. 5 | P a g e Case Study 2 | Show the teacher five pieces of square tiles. Make a shape using five square tiles. There are some rules that we have to follow.
  • 6. 6 | P a g e Whole Number Addition and Subtraction |Session 2  Materials  Strategies  Semantics  Variation Semantics  Part-Whole  Change  Comparison Case Study 2 | Together, Jon and Kim have 32 coins. Jon has 19 coins. Find the number of coins that Kim has.
  • 7. 7 | P a g e Case Study 3 | Lance has 10 coins more than Ming. Together, they have 34 coins. How many coind does Lance have?
  • 8. 8 | P a g e Case Study 4 | At first, Lance had 10 coins more than Ming. Then Ming gave Lance 6 coins. Who had more coins in the end? How many more?
  • 9. 9 | P a g e Open Lesson for Rising Second Graders |Session 3 What do we want the students to learn? Lesson Segment Observation / Question How can we tell if students are learning? What help students who struggle? What are for students who already know what we want them to learn? Summary
  • 10. 10 | P a g e Use of Activities for Math Learning |Session 4 Types of Lessons  To develop basic ideas, concepts and skills  To consolidate basic ideas, concepts and skills  To extend basic ideas, concepts and skills Case Study 5 | Use the digits 0 to 9 not more than once to make an addition equation.
  • 11. 11 | P a g e Holistic Assessment for Young Learners |Session 5 Assessment Benchmarks  Approaching Expectations  Meeting Expectations  Exceeding Expectations Students should be able to perform rational counting. Approaching Expectations The student is unable to count a plate of not more than ten cookies.  Can the student perform one to one correspondence?  Can the student classify?  Can the student rote count?  Has the student grasp the principle of cardinality? Meeting Expectations The student is unable to count a plate of not more than ten cookies.  Also able to read the correct numeral  Also able to read the correct number word  Also able to write the correct numeral  Also able to write the correct number word Exceeding Expectations The student is unable to count a plate of not more than ten cookies. The student is also able to read and write the correct numeral and number word.