Learning and Mathematics

Bluebook Anticipatory Set-Multiple choiceLearning and Writing cont.Learning and MathematicsDiscussions–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)

01

23

45

67

89

10

None Generating Listing Outlining

Quality

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 1st draft

2.9 .38 .43

Unpolished 1st draft

8.0 .85 .23

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

RereadRevise 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/writer Listener/Helper

Come with a purpose Read my story to L/H Listen while the R/W readsTalk and ask questions Look at the writing

Help Revise and EditGive

ComplimentsAsk QuestionsMake Suggestions

Error Detection in Writing

Referent Errors Syntax Errors

Writer’s own text

17% 53%

In other texts 73% 88%

Bartlett, 1982

The Writing Process

PlanningConferencin

g

Reviewing

Translating(draft) Final

Copy

Scaffolding Student Writing

Building Early Literacy Skills The use of mediators Inventive spelling

1. Non-alphabetic markings2. Initial sounds – semi-phonetic3. Initial and final sounds - phonetic4. Medial vowels - transitional5. 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 ApproachesProblem Solving in MathematicsCounting Understanding NumberMathematical EquivalenceLogical 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

Area Experts Novices

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.

Planning Plan carefully before attempting a solution to novel problems.

Plan briefly then quick adopt and try solutions.

Monitoring Demonstrate 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 – 100 0 – 1000 0 100

0 100

100

Estim

ate

Actual magnitude 0 100

100

Estim

ate

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: 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 + _____

Logical Reasoning Skills

Piaget’s Formal Operations Stage

Changing Strategies and Rules Siegler

Questioning Strategies

Blooms Taxonomy (1956)KnowledgeComprehensionApplicationAnalysisSynthesisEvaluation

Anderson & Krathwohl (2001)RememberUnderstandApplyAnalyzeEvaluateCreate

Learning and Mathematics

Bluebook Anticipatory Set-Multiple choiceLearning and Writing cont.Learning and MathematicsDiscussions–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