Elementary Mathematics Methods Chapter 3 - Notes

Chapter 3 Teaching for Problem Solving • • • • • • Teaching a skill so can later problem solve Learn abstract concept, then solve as way to apply skills Used in many textbooks Need prior knowledge to understand explanations Usually presented one way May say only one way to solve a problem Teaching about Problem Solving • • Teach how to problem solve – process or strategies Draw a picture Teaching Through Problem solving • • • real contexts, problems, etc. build meaning present problem at beginning and work through Four Steps for Problem Solving1. • • • • understand problem2. devise a plan on how to solve it carry out plan look back (does the answer make sense?) Strategies • • • • • • draw a picture, act out, use a model look for a pattern guess and check make a table or chart try a simpler form of problem make a list Features of a Problem • • begin where students are requires justifications and explanations for answers and methods General Questions for Understanding • • • • what did you do to help yourself understand? Remind of other problems Irrelevant information? How did you know it’s not important? How did you decide what to do? How did you decide the right answer? Writing in Math • • • • Reflective Rehearsal for discussion Record for when lesson is done RTI Tier 1 – all students • • Tier 2 – didn’t meet level one but not considered for SPED Tier 3 – one on one Strategies • o Tier 1 Flexible grouping Chapter 3 o o o o Monitor progress Active involvement High expectations Multiple representations • Tier 2 o Individual diagnostic interview o Collab with sped teacher o Focus on big ideas o Think aloud o Model behavior so Peer assisted learning o Steps written o Supply families with additional materials o Teach test-taking strategies Before o o o State purpose and new vocabulary Clarify concepts from prior knowledge Define tasks of group members During o o Lay out directions Give guiding questions o Summarize After Five Adaptations 1. Accommodations 2. Different instructions 3. Learning centers 4. Tiered lessons 5. Flexible grouping • Before o Activate prior knowledge – simple version of task o Be sure problem is understand o Establish clear expectations • During o Allow to work without much guidance o o o Notice math thinking (ask to explain actions) Provide appropriate support Extensions • After o Listen actively without evaluating o Summarize main ideas and identify future problems Drills are appropriate when • • Concepts and meanings are fully developed Flexible and useful procedures have been developed Chapter 3 • Speed and accuracy are needed