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

Good Writers Have….. Knowledge Language Topic Audience

Cognitive Processes in Writing The writing process

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

Effects of Planning on Written Work (Kellogg, 1994)

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

Conservation of number

Numerical Magnitude Number line estimates 0 – – Estimate Actual magnitude0100 Estimate Actual magnitude Siegler & Booth, 2004

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

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

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

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

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