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OUTLINE Rationale of the MiGen project (5 mins ) What is the MiGen system? (5 mins )

The MiGen system and its impact on students and teachers: a review of the research dilemmas and positive outcomes through the eyes of a teacher and a researcher Eirini Geraniou (Institute of Education) Helen Humble (Amery Hill School). OUTLINE Rationale of the MiGen project (5 mins )

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OUTLINE Rationale of the MiGen project (5 mins ) What is the MiGen system? (5 mins )

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  1. The MiGen system and its impact on students and teachers: a review of the research dilemmas and positive outcomes through the eyes of a teacher and a researcher Eirini Geraniou (Institute of Education) Helen Humble (Amery Hill School) http://www.migen.org

  2. OUTLINE • Rationale of the MiGen project (5 mins) • What is the MiGen system? (5 mins) • Research Methodology (5 mins) • Two student case studies(10-15 mins) • Our Dilemmas and Positive Outcomes (5 mins) • Discussion (15-20 mins) • Final Remarks (5 mins) http://www.migen.org

  3. Generalisation as… the process of identifying and expressing relationships that underpin pictorial patterns 2(w + 2) + 2h For n red squares, there are 3n + 1 blue and 2n + 2 green squares http://www.migen.org

  4. Students’ Difficulties Students are often taught methods of finding the ‘general’ rule using the term-to-term method and fail to conceptualise relationships between variables, justify them and use them in a meaningful way “Pattern-Spotting” Specific/General case Tasks presented on paper encourage students to focus on the specific case and fail to see the general case through the particular examples Mathematical Language Students struggle to understand how to use letters to represent any value and how to use mathematical notations to express generality. Also, they can articulate the recursive rule, but not the algebraic one. Linear Scaling “How many tiles for n=6? How many tiles for n=12?” “How many tiles for n=10? How many tiles for n=100?”

  5. AIM • - to co-design, build and evaluate • with teachers and teacher educators • a pedagogical and technical environment for improving 11-14-year-old students’ learning of algebraic generalisation http://www.migen.org

  6. The MiGen system comprises: • - a microworld (eXpresser) • - Intelligent support for students using eXpresser • Teacher Assistance tools http://www.migen.org

  7. A MiGen task Task Question Construct the Train-Track model. Use more than one pattern to make the model. Use different colours for each pattern to show other people how you made your model. Find a rule for the number of tiles for any model. Share your rule and match it with your model. Collaborative Task Convince each other that your model and rules are correct Can you explain to each other why the rules look different but are equivalent? Discuss and write your explanations. http://www.migen.org

  8. Addressing students’ difficulties • “Pattern-Spotting” • Encourage students to look for the structure of the pattern to help them derive a general rule • Specific/General Case • (Randomised) Animated Task Presentation • Mathematical Language • Students with the help of the eXpresser language develop an understanding of the notions of variables and constants and make the transition to symbols easier • Linear Scaling • The MiGen activities provide opportunities for engaging with counterexamples http://www.migen.org

  9. Research Methodology • In general • Iterative Design • Feedback from students • Close collaboration with teachers (& teacher educators) • In Particular • Amery Hill School • Sample • (year 7 – July 2009 – 16 students) • (year 8 – July 2010 – 16 students)  (year 9 – Nov 2010 – 30 students) • Activity Sequence • Introductory Tasks – Individual Tasks – Collaborative Tasks –Classroom Discussion • Individual PCs http://www.migen.org

  10. Research Methodology Data Collection • Audio record (teachers and researchers’ interventions, students’ collaboration and task-based interviews) • Video record classroom sessions Dialogue between teacher-researcher • Before, during and after each session Teacher’s role • Organise sessions, find students, introduce the system, explain the tasks, run classroom discussions, intervene when needed to support students, inform research team of students’ learning profiles Researcher’s role • Support the teacher in the organisation of the studies, design activities in collaboration with the teacher, write a suggested lesson plan, familiarise teacher with the system, technical support during lessons, inform teacher of previous research studies and results http://www.migen.org

  11. Student case studies:Steve and Laura • Construct models • Show intelligent support • Grouping Tool http://www.migen.org

  12. eXpresser – Train Track task http://www.migen.org

  13. Steve’s model

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  31. List of prompts (Steve) • Draw Attention/ Nudge • “There are no unlocked numbers” (Comment) • “The pattern is not coloured because you need the exact number of tiles in the pattern” (Hint) • Create Cognitive Conflict/Challenge • “Your pattern might not be coloured for a different number of building blocks” (Comment) • Reflection • “How many tiles does the building block have? How many building blocks does your pattern have?” (Question) • “That’s correct but what is the link between these numbers?” (Question) http://www.migen.org

  32. Laura’s model • Add messing-up in the General Model...

  33. Laura’s model • Add messing-up in the General Model...

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