Learning How to Learn Mathematics

1. Learning How to Learn Mathematics Wade Ellis, Jr. West Valley College (retired) wade25@sbcglobal.net

2. The Ability of Students to Learn We are all trying to improve student performance. We spend lots of time and effort on improving the material we present (textbooks, handouts) and our ability to present it using modern approaches. These efforts are valuable and should continue. However, we do not spend much time working on improving students’ ability or capacity to learn mathematics. That’s what I’d like to talk about today.

3. Outline • Introduction • Jim Stigler: students need to be engaged in • Productive Struggle, Explicit Connections, Deliberate Practice • Learning is a Process • Mathematics Classroom Culture – 14 Aspects • Developmental Math Learning Risk Factors • Key Learner Characteristics for Math Success • The Learning Process Methodology for Math • An example: Analyzing a Function • L2L Math Camp/Course – Recovery Course • Questions and Comments

4. Learning is a Process • Anyone’s learning process can be improved • How can we help students improve theirlearning process? • Purpose of Assessment vs. Evaluation Feedback Assessment is to improve performance Evaluation is to judge to punish or reward • SII: Strengths, Areas for Improvement, Insights

5. Learning is a Process that Can be Improved

6. Major Areas of Process Education

7. Mathematics Classroom Culture – 14 Aspects (pages 2-5) • Measurement • Ownership • Relationship • Scope of Learning • Self-Awareness • Social Orientation • Transparentcy • Challenge • Cognitive Complexity • Control • Delivery • Design • Efficacy • Feedback

8. Common Risk Factors for All Development Students (first page) • Lacks Self-Discipline • Afraid of Failure • No Sense of Self-Efficacy • Unmotivated • Fixed Mindset • Teacher Pleaser • Unchallenged (bored) • Memorizes Instead of Thinking • Doesn’t Transfer or Generalize Knowledge • Highly Judgmental • Minimal Meta-cognitive Awareness • Insecure Public Speaker

9. Risk Factors Specific to Development Math Students (first page) • Placement in Courses • Students’ Current Learning Process • Prerequisite Knowledge • Reading Mathematics • Critical Thinking Skills • Willingness to Struggle • Problem Solving • Misconceptions

10. Classroom Practices • Assessment: SII • Strengths, Areas for Improvement, Insights • Reading logs and how to use them • Questions at the beginning of class • Ask students to give reasons for the steps you do at the board

11. Steps Say your becauses.

13. Common Key Characteristics for Academic and Math Success • Thinks Critically • Validates • Generalizes • Persists • Speaks Publicly • Focuses • Uses Meta-cognition

14. Characteristics of a Profile of a Quality Mathematical Collegiate Learner (p6) • Mindset • Reasoning • Thinking • Modeling • Learning • Problem Solving • Communications

15. Reasoning • Make Conjectures • Seek Counter • Examples • Are Logical • Identify Dead Ends Mindset • Are Skeptical • Are Precise • Enjoy Productive Struggle • Are Self-reliant

16. Modeling • Build Models • Are Tool Users • Innovate • Manipulate Data Thinking • Abstract • Visualize • Use Multiple Representations • Make Connects

17. Problem Solving • Identify & Define Problems • Identify Key Issues • Identify Assumptions • Reuse Solutions Learning • Interpret Notation • Analyze Examples • Think Analytically • Transfer Knowledge

18. Communicating • Translate • Teach • Think on Your Feet • Build Vocabulary

19. Learning Process Methodology

20. Importance of LPM • Authors: design of materials • Faculty: facilitation of learning • Students: learning process • Course assessors: measurement to improve • Learning of content • Improvement of learning skills

21. Learning Process Methodology (LPM) • Why • Orientation • Prerequisites • Learning Objectives • Performance Criteria • Vocabulary • Information • Plan • Models/Examples • Critical Thinking Q’s • Applications • Problem Solving • Self-assessment • Research

22. LPM Plan Models CTQs Applications Problem Solving Self-assessment Research • Why • Orientation • Prerequisites • Learning Objectives • Performance Criteria • Vocabulary • Information

23. LPM Adapted for Mathematics (p8) • Purpose • Discovery • Expectations for Learning • What do you already know? • Required math language • Information needed for learning • Learning Resources (data sets, software tools, simulations, etc.) • Why • Orientation • Prerequisites • Learning Objectives • Performance Criteria • Vocabulary • Information

24. LPM Adapted for Math (cont’d) • Plan • Models • CTQs • Applications • Problem Solving • Self-assessment • Research • Classroom Activity • Summarize and Review Steps 1-7 • Plan • Models • Critical Thinking Questions • Performance Criteria • Demonstrate Your Understanding • Hardest Problem – Generalize Knowledge • Making it Matter – Problem Solving • Identify and Correct the Errors - Content • Learning to Learn Mathematics – Discipline • Assess Learning Performance – Learning Process

25. An Example • Analyzing a Function Section 2.5 ofQuantitative Reasoning and Problem Solving • Companion Website

26. Learning to Learn Math Camp Agenda Agenda

28. L2L Experiences

29. FOA

30. What are your comments and questions?

31. http://www.processeducation.org/peconf/index.html

32. References and Links • Pathfinder for 25 Years of Process Education Scholarship - http://www.processeducation.org/ijpe/2016/pathfinder/ • Risk Factors - http://www.processeducation.org/ijpe/archive.htm • Seventh Edition (2015) Last article • 8 Additional Risk Factors for Math – in handout • LPM for Mathematics-in handout • Academy of Process Education’s International Journal of Process Education -http://www.processeducation.org/ijpe/archive.htm

33. References and Links (cont’d) • PQCL diagram -http://www.pcrest.com/PC/Reflections/issue28/graphic2a.jpg • Key Characteristics for Academic Success paper, including PQCL - http://www.processeducation.org/ijpe/2016_2/2016_success2.pdf • Learning to Learn Camp – http://www.learningtolearncamp.com/ • Recovery Course - http://pcrest.com/recovery/

34. References and Links (cont’d) • Transformation of Education Learning Object – http://www.transformation-of-education.com/ http://www.processeducation.org/ijpe/2011/transformationh.pdf • Timeline for PE Scholarship –http://www.processeducation.org/ijpe/25/timeline/ • Learning to Learn: Becoming a Self-Grower – http://www.pcrest.com/L2L/L2L_flyer2.pdf • Quantitative Reasoning and Problem Solving – http://pcrest.com/PC/pub/2014/QRPS_course_design.pdf

35. Additional Slides • Here are a set of slides on the description of each aspect of the Transformation of Education, but not presented during the talk.

36. What is a Mathematics Education Culture? • Challenge: The degree to which increasing the level of difficulty is used in order to grow capacity for learning and performing • Cognitive Complexity: The degree to which training and doing is elevated to problem solving & research • Control: The locus of power/authority for the learning situation or experience

37. Math Culture (cont’d) • Delivery: The means by which information/knowledge is obtained by learners • Design: The purposeful arrangement of instructional environment, materials, and experiences to support learning • Efficacy: The well-founded belief in one's capacity to change and to make a difference • Feedback: Information about what was observed in a performance or work product

38. Math Culture (cont’d) • Measurement: The process of determining the level of quality surrounding a performance or product • Ownership: The degree to which the learner accepts responsibility and accountability for achieving learning outcomes • Relationship: The degree of emotional investment an instructor or mentor has in his or her students or mentees

39. Math Culture (cont’d) • Scope of Learning: The contexts across which learning occurs and its application is demonstrated • Self-awareness: The degree to which reflective and self-assessment practices are used by the individual to foster the growth of his or her earning skills across the cognitive, affective, and social domains

40. Math Culture (cont’d) • Social Orientation: The investment, interdependence, and responsibility for learning throughout a community • Transparency: The degree to which stakeholders can view individual, team or collective performance