CONCRETE MODELS OF GOOD
MATH INSTRUCTION
ESC Region 13
Inclusion Institute 2014: Great Expectations
Misty Terrell
[email protected]
512.919.5206
JC Sanders
[email protected]
512.919.5240
Explicit and Systematic
C-V-A sequence
Good Math Instruction
Manipulatives
Real-life situations
Strategy-based
Overview
Table 2. Recommendations and corresponding levels of evidence
Recommendation
Level of evidence
Tier 1
1. Screen all students to identify those at risk for potential mathematics
difficulties and provide interventions to students identified as at risk.
Moderate
Tiers 2 and 3
2. Instructional materials for students receiving interventions should
focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8.
These materials should be selected by committee.
Low
3. Instruction during the intervention should be explicit and systematic.
This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and
frequent cumulative review.
Strong
4. Interventions should include instruction on solving word problems
that is based on common underlying structures.
Strong
5. Intervention materials should include opportunities for students to
work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of
mathematical ideas.
Moderate
6. Interventions at all grade levels should devote about 10 minutes in each
session to building fluent retrieval of basic arithmetic facts.
Moderate
7. Monitor the progress of students receiving supplemental instruction
and other students who are at risk.
Low
8. Include motivational strategies in tier 2 and tier 3 interventions.
Low
Source: Authors’ compilation based on analysis described in text.
(6)
Principles of Instruction
“Our working memory, the place where we process information, is small. It can only handle a few bits
of information at once—too much information swamps our working memory.” (p. 13)
“It is important that students achieve a high success rate during instruction and on their practice
activities. Practice, we are told, makes perfect, but practice can be a disaster if students are practicing
errors! If the practice does not have a high success level, there is a chance that students are practicing
and learning errors. Once errors have been learned, they are very difficult to overcome.” (p. 17)
“The development of expertise requires thousands of hours of practice, and daily review is one
component of this practice.” (p. 13)
Rosenshine, B. Principles of Instruction: Research-based strategies that all teachers should know. American
Educator , Spring 2012, 12-19, 39.
IDEAS FOR INTERVETIONS
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Equals - http://www.ablenetinc.com/Curriculum/Equals-Mathematics-Program
Factastic Math Strategy System – http://store.esc13.net
Moving with Math - http://www.movingwithmath.com
ESTAR - http://www.epsilen.com/crs/12111739
MSTAR –
o Equivalent fractions: http://www.epsilen.com/crs/1011427
o Facts and patterns, mult/div: http://www.epsilen.com/crs/1012499
o Proportionality: http://www.epsilen.com/crs/1116059
o Ratio and rates: http://www.epsilen.com/crs/1012676
ESED - http://www.epsilen.com/crs/12111737
Numicon - www.numicon.com
Center for Intensive Intervention: Academic Intervention Program Tools Chart
http://www.intensiveintervention.org/resources/tools-charts