1. Learning and Mathematics Bluebook Anticipatory Set-Multiple choice Learning and Writing cont. Learning and Mathematics Discussions–Questioning Strategies For Tuesday: Read Chapter 6, HYLA1 due

2. Good Writers Have….. Knowledge Language Topic Audience

3. Cognitive Processes in Writing The writing process

4. Planning in Writing Parts of planning Generating Organizing Goal-Setting Global v. local planning Pianko study

5. Effects of Planning on Written Work (Kellogg, 1994)

6. Translating (draft writing) Write for ideas first then update focus Don’t be ‘Constrained’ by  Graphic- layout, spacing, spelling  Syntactic- grammar, punctuation, sentence organization  Semantic- convey intended meaning  Textual- sentences fit to create a cohesive paragraph  Contextual- appropriate style

7. Research on Draft Writing Total Number of Arguments Arguments per Sentence Mechanical Errors per Sentence Polished 1 st draft 2.9.38.43 Unpolished 1 st draft 8.0.85.23 Glynn et al., (1982)

8. Implications for instruction (translating phase of writing) Constraints of writing process can inhibit the process Mechanics Spelling Penmanship This can load the working memory beyond capacity and interfere with high-level planning. Older writers/ more experienced writers are more automatic with mechanics, integration and completion of ideas

9. Reviewing Reread Revise and Edit now focus on  Graphic, syntactic, semantic and textual norms  Contextual fit

10. Conferencing An external reviewer Again focus on  Graphic, syntactic, semantic and textual norms  Contextual fit

11. Reader/writerListener/Helper Come with a purpose Read my story to L/HListen while the R/W reads Talk and ask questionsLook at the writing Help Revise and Edit Give Compliments Ask Questions Make Suggestions

12. Error Detection in Writing Referent ErrorsSyntax Errors Writer’s own text 17%53% In other texts73%88% Bartlett, 1982

13. The Writing Process Planning Conferencing Reviewing Translating (draft) Final Copy

14. Scaffolding Student Writing Building Early Literacy Skills The use of mediators Inventive spelling 1. Non-alphabetic markings 2. Initial sounds – semi-phonetic 3. Initial and final sounds - phonetic 4. Medial vowels - transitional 5. Moves toward conventional spelling

15. Scaffolding Student Writing Building Early Literacy Skills The use of mediators Inventive spelling Using Rubrics As a guide In grading

16. Learning and Mathematics Instructional Approaches Problem Solving in Mathematics Counting Understanding Number Mathematical Equivalence Logical Reasoning

17. Bottom-up vs. Top-down Processing Bottom-up start with the most basic units or elements and build up Top-down proceeds from information already stored in memory (prior knowledge) to decipher new input

18. Learning Mathematics Two approaches to instruction Bottom up (code first): Intensive drill and practice on the basic building blocks  i.e., correct procedures for adding, subtracting, multiplying, and dividing Top down (meaning first): Learning should begin with problems that draw upon children’s real-world experience and that include exposure to mathematical principles  Encouraged to justify their reasoning, solicit help from others, and share what they have learned

19. A Problem to Solve Martha has 25 eggs while Mark has only 15 eggs. If they were to combine and then package their eggs to sell by the dozen, how many packages could they sell?

20. Problem Solving in Mathematics Problem Translation Linguistic and Factual knowledge Problem Integration Schematic knowledge Solution planning and monitoring Strategic knowledge Solution Execution Procedural knowledge

21. Expert v. Novice Problem Solvers AreaExpertsNovices Translation & Integration (representing problems) Focus on structural features. Search for context, underlying principles and relationships in problems. Focus on surface features. See problems in isolated pieces. PlanningPlan carefully before attempting a solution to novel problems. Plan briefly then quick adopt and try solutions. MonitoringDemonstrate well developed metacognitive abilities; abandon inefficient strategies Limited metacognition; persevere with unproductive strategies

22. Counting and the Base 10 system Fuson et al (1990) English Asian Languages

23. Conservation of number

24. Numerical Magnitude Number line estimates 0 – 100 0 – 1000 0100 0 Estimate Actual magnitude0100 Estimate Actual magnitude Siegler & Booth, 2004

25. Understanding Mathematical Equivalence School aged children (age 7 -11) have difficulty learning to interpret the equal sign as a relational symbol Reason: 3 + 2 = 5; operation = answer Instead, they interpret = sign to mean “calculate a total” Leads to difficulty when faced with non- conventional problems. I.e. 3 + 2 = 4 + _____

26. Logical Reasoning Skills Piaget’s Formal Operations Stage Changing Strategies and Rules Siegler

27. Questioning Strategies Blooms Taxonomy (1956) Knowledge Comprehension Application Analysis Synthesis Evaluation Anderson & Krathwohl (2001) Remember Understand Apply Analyze Evaluate Create

28. Learning and Mathematics Bluebook Anticipatory Set-Multiple choice Learning and Writing cont. Learning and Mathematics Discussions–Questioning Strategies For Tuesday: Read Chapter 6, HYLA1 due

29. “It is better to ask some of the questions than to know all the answers.” - James Thurber