Learning and Science Mathematics cont.  Bluebook Anticipatory Set  Learning and Mathematics cont.  Discussions–Questioning Strategies  Learning and Science  Current Issue Journal Article for D2L For Thursday: Quiz #1, Current Issue Journal Article topic approval by Oct. 12th

Bluebook Anticipatory Set  Review all previous types of assessment (strengths and weaknesses in each charts) and describe how you would create an assessment for Quiz #1 (Chap. 1-6).  How would you divide the 25 pts.?  What kinds of questions would you use?  How would you divide the chapters? Justify your response…

Problem Solving in Mathematics  Problem Translation Linguistic and Factual knowledgeLinguistic and Factual knowledge  Problem Integration Schematic knowledgeSchematic knowledge  Solution planning and monitoring Strategic knowledgeStrategic knowledge  Solution Execution Procedural knowledgeProcedural 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

Conservation of number

Questioning Strategies Blooms Taxonomy (1956) KnowledgeComprehensionApplicationAnalysisSynthesisEvaluation Anderson & Krathwohl (2001) RememberUnderstandApplyAnalyzeEvaluateCreate

Science “The whole of science is nothing more than the refinement of everyday thinking.” Einstein

Science Before we talk about learning science, let’s take a few minutes to think about our experiences with science. Here’s a little writing task. Write your response to the following:

Science 1) Describe a scientific misconception you held at one time. 2) What was the source of this misconception? 3) How long did you hold this misconception? 4) How did you come to a new understanding?

Mental Representations are: The symbol structures we construct to encode our experiences, process them, and store them (schema).  The symbolic links between the external environment and our internal mental world

Mental Representations  The representations we construct in encoding our experiences have profound effect on our behavior and our learning.

Learning in Science A traditional view of science Learning in science is similar to learning in other areas. Learning in science also differs in some important ways.

Conceptual Change Model  Learners enter science instruction with many pre-existing misconceptions or incomplete representations that can conflict with the teacher’s teaching of scientific concepts.

Goal of Conceptual Change  Learners must replace their misconceptions with new conceptions -that is, they must find new mental models that explain observations (data) better than the previous ones. -that is, they must find new mental models that explain observations (data) better than the previous ones. -Piaget called this accommodation

Science In addition as part of the- Conceptual Change Model Students need to develop scientific thinking skills, such as how to use their conceptions to solve problems.

Steps Toward Conceptual Change Changing misconceptions to more accurate conceptions involves multiple processes. Recognizing an Anomaly Discarding a Misconception Constructing a New Model Using a New Model Learning to Build & Use Scientific Knowledge

Stages in Conceptual Change Conceptual change isn’t easy, but does follow a predictable course.

Stages in Conceptual Change  Initial discomfort  Attempts to explain away  Attempts to adjust observations  Doubt  Vacillation  FINALLY, conceptual change

Learning and Science Mathematics cont.  Bluebook Anticipatory Set  Learning and Mathematics cont.  Discussions–Questioning Strategies  Learning and Science  Current Issue Journal Article for D2L For Thursday: Quiz #1, Current Issue Journal Article topic approval by Oct. 12th

Quiz #1  Chapters 1-6 in the text  Table of Contents/Summaries  PP Presentations (electronic syllabus)  Assessment Item Analysis  Multiple Items (some of each to match different learning styles)  No time limit

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