edspe 523 week one. reading/math parallels explicit instruction vs. whole language decoding vs....
Post on 29-Dec-2015
220 Views
Preview:
TRANSCRIPT
Reading/Math Parallels
Explicit Instruction vs. Whole Language
Decoding vs. Comprehension
Phonemic Awareness
Scientifically based instruction vs. Philosophy based instruction
Teacher-Directed vs. Guided Discovery
Computation vs. Problem Solving
Number Sense Scientifically
based instruction vs. Philosophy based instruction
Proficiency in Math
Conceptual understanding Comprehension of mathematical concepts,
operations, and relations Procedural fluency
Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Strategic competence Ability to formulate, represent, and solve
mathematical problems Adaptive reasoning
Capacity for logical thought, reflection, explanation, and justification
Productive disposition Habitual inclination to see mathematics as sensible,
useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
(National Research Council, 2001, p. 5)
Agenda
How are we doing in math? In general For students with special needs
How prepared are teachers? How good are our curricula (texts)? What does the research tell us about
effective practices in math?
Student Performance (NAEP) National Assessment of Educational
Progress (NAEP) given at 4th, 8th, & 12th grades “The Nation’s Report Card”
NAEP 8th Grade Math (2003)
33
40
27
0%
20%
40%
60%
80%
100%
Prof/Adv
Basic
Below Basic
Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)
NAEP 8th Grade Math (Race/Ethnicity)
61 53 46
21 23
3236
38
43 35
7 11 1636 42
0%
20%
40%
60%
80%
100%
Black Latino Native White Asian
Prof/ Adv
Basic
Below Basic
Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)
NAEP 8th Grade Math (Family Income)
53
22
36
41
11
37
0%
20%
40%
60%
80%
100%
Poor Not Poor
Prof/Adv
Basic
Below Basic
Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)
Student Performance (TIMSS) The Third International Mathematics and
Science Study (TIMSS), a cross national comparative achievement test for students (approximately) 9 and 13 years old
TIMSS
TIMSS
(9 year olds)
2 countries scored significantly higher than U.S. students
TIMSS
(13 year olds)
24 countries scored significantly higher than U.S. students
Student Performance (PISA)
Program for International Student Achievement (PISA) cross-national study of 15-year olds in 32 industrialized countries
2003: U.S. Ranked 24th out of 29 OECD Countries in Mathematics
300
350
400
450
500
550
Ave
rag
e S
cale
Sco
re
Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results , data available at http://www.oecd.org/
U.S. Ranks Low in the Percent of Students in the Highest Achievement Level
0
2
4
6
8
10
Per
cen
t o
f S
tud
ents
Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at http://www.oecd.org/
Washington--WASL
Grade Level Math
3rd Grade 69.6%
4th Grade 58.1%
5th Grade 59.5%
6th Grade 49.6%
7th Grade 54.6%
8th Grade 49.8%
10th Grade 50.4%
2006-07
Math and Students with Special Needs Not as much information
Adolescents with LD may perform up to 7 years behind their grade level in math (Cawley & Miller, 1989)
Only 12% of students with mild disabilities participate in advanced math classes (Wagner & Blackorby, 1996)
Performance Deficits
Younger Students Lack fluent and accurate recall of number
combinations Continue to use counting strategies after other
students have attained fluency However, more likely to make errors with these
strategies Deficit may be stable over time (little
improvement over 2years) Difficulty in quantity discrimination
Bigger/smaller, how much bigger
Performance Deficits
Older Students Difficulty developing and applying
strategies May use same strategies , but less efficiently May apply strategy correctly, but to the wrong
problem type May be reluctant to give up initial strategies
and replace with more efficient ones Difficulty mastering basic operations
Teacher Knowledge
Liping Ma compared Chinese and U.S. teachers’ knowledge of mathematics and mathematics instruction.
Ma, 1999Ma, 1999
Teacher Knowledge
Findings: Teachers’ mathematical knowledge directly
affects their students’ mathematical learning.
Teacher Knowledge
Findings: U.S. teachers displayed procedural
knowledge with some algorithmic competence.
Chinese teachers displayed algorithmic competence with conceptual understanding.
Teacher Knowledge
Factors that support the development of Chinese teachers’ Profound Understanding of Fundamental Mathematics (PUFM): their own elementary education their teacher preparation their work as math specialists
Teacher Knowledge
Ma’s recommendations: refocus teacher preparation enhance teacher study of mathematics “on
the job” use well-constructed textbooks
Mathematics Curricula
Mathematics curricular materials (textbooks) account for about 75% of what occurs in mathematics instruction in elementary and secondary classrooms.
Porter 1989
Mathematics Curricula
U.S. textbooks compared to those of other countries: much larger and heavier cover more topics with less depth fail to develop linkages between topics are repetitive and spiral
Schmidt, Houang, & Cogan, Schmidt, Houang, & Cogan, 20022002
Mathematics Curricula
U.S. textbooks compared to those of other countries: focus more on “eye catching,” irrelevant
illustrations, dedicate equal time to simple and difficult
tasks, provide little information for teachers on
content and methodology.
Schmidt, Houang, & Cogan, 2002
Scientifically Based Instruction Reading [math] programs based on
scientifically based research incorporate the findings of rigorous experimental research.
Slavin, 2003
Relevant Reviews of Mathematics Research Teacher Effectiveness Research Direct Instruction Research, Follow
Though and Beyond Recent Reviews of Research:
Students At Risk for Academic Failure (Baker, Gersten, & Lee, 2002)
Students with Learning Disabilities (Gersten et al., under review)
Reviews of Research on Mathematics for Students At Risk Fifteen high quality studies resulting in
four major interventions that improved student achievement: Progress-monitoring data available to
teachers and students Peer tutoring Providing feedback to parents Explicit, teacher-directed instruction
Reviews of Research on Mathematics for Students with Learning Disabilities Twenty-six high quality studies in three
categories: Curricular and broad instructional
approaches—use of diagrams and visual scaffolding, use of explicit instruction including self-verbalization
Progress monitoring Tutoring
Other Critical Instructional Elements Highlight Big Ideas Address Prior Knowledge Content and Example Sequencing Example Selection Diagnosis and Error Correction Practice and Review
Special Education: Underlying Assumptions Special education programs are a
problem-solving component of the school system whose function is to identify and serve individuals whose performance is significantly discrepant from their peers. (Deno)
top related