learning and mathematics bluebook anticipatory set-multiple choice learning and writing cont....
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Learning and Mathematics
Bluebook Anticipatory Set-Multiple choiceLearning and Writing cont.Learning and MathematicsDiscussions–Questioning Strategies
For Tuesday: Read Chapter 6, HYLA1 due
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
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
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 + _____
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