Secondary Mathematics · Merion School District math curriculum –it is not our curriculum. •...

Secondary MathematicsLower Merion School District

The goals of this presentation are to

provide:

Information regarding the secondary math

curriculum and College Preparatory Math

program

Research on best practices in math as

evidenced in CPM

Data regarding the CPM implementation

Information on the revised math sequence

Where are we now?

Grades 6 to 8

Concepts maps have been developed for each unit of

instruction.

Implementation of CPM to support District curriculum in all

courses except Algebra 1 and Geometry (at grade 8)

Grades 9 to 12

Currently developing concept maps for each unit of

instruction

Working toward the development of common final

assessments between both buildings based on the

essential understandings for each course.

Use of CPM as the primary resource in Algebra 1 (LM)

and Algebra 1, Geometry and Algebra 2 (HH)

Background - CPM

• Has been used for a number of years by some of our teachers

• Initially used as resource to address the needs of students who were consistently not meeting the grade level expectations in mathematics and understanding fundamental concepts in math

• Teachers using it found that this resource would benefit all children as it provided a balance focusing on integrating basic skills and topics with conceptual understanding and problem solving.

Background of CPM

• Summer 2008 - secondary teacher representatives met

with the math curriculum supervisor to discuss the use of

the CPM program and gather feedback, input and

suggestions.

• Came to consensus that it would be beneficial to move

forward with a more consistent implementation of the math

program to support the district math curriculum and create

continuity. Suggestions were made by the group to put in

place during the implementation.

• A proposal for moving forward with a more consistent

implementation of CPM was presented at the Curriculum

Committee of the Board – Fall of 2009.

• Information was again presented at meetings in March,

April, and May in 2010.

College Preparatory Math

• College Preparatory Math is the primary resource/program

that is being used to support the delivery of the written Lower

Merion School District math curriculum – it is not our

curriculum.

• The K-12 Mathematics scope and sequence has been

reviewed and refined with a focus on alignment to the

Pennsylvania anchors and standards and will continue to be

reviewed as we move toward the Core Math Standards.

• The CPM program has been evaluated in terms of how it

addresses the state and district math

expectations/curriculum and supports best practices in math

as outlined by the National Council of Teachers of

Mathematics, the National Research Council and brain

research.


Focus on deeper explorations and problem solving for all

students through meaningful and engaging mathematics with

an emphasis on reasoning and application

Emphasis on developing the basics while encouraging students

to understand ideas, see relationships between them, and apply

mathematical principles to complex problems and real world

models

Focus on students making sense of mathematics and

understanding mathematics followed by on-going practice

Incorporates a variety of teaching methodologies (lectures,

whole class discussions, manipulatives, teams)

Direct instruction is provided based on teacher observations of

students. Guidance is also provided for students when they

work in teams or pairs.


CPM – resource that will allow different ways into the

problems so that students of different strengths and

experiences will be able to engage in the problem.

Expectations will remain high and students will be

appropriately challenged through the core curricular

resource and additional supplemental/enrichment materials.

Incorporates research based best practices – Teaching for

understanding; collaborative work; problem-based learning;

mathematical communication (oral and written)

.

Educator’s Guide

What Works in Teaching Math?

Researchers

Robert Slavin – John Hopkins University

Cynthia Lake – John Hopkins University

Cynthia Groff – University of Pennsylvania

Funded by the Institute of Education

Sciences, U.S. Department of Education

Conclusions

• No evidence that different curricula give different

outcomes in terms of achievement.

• Strong evidence that using effective teaching

strategies can make a difference in particular

cooperative learning.

• The programs that produce consistently positive

effects on achievement are those that

fundamentally change what students do every

day in their core math classes.

Implications of Brain Research for

Teaching Young Adolescents

• Source – Middle School Journal Research Articles

• Neuroscience research on adolescent brain

development

Implications for the Classroom:

Posing word problems to challenge thinking so that

students learn that there are many ways to solve a

problem.

Using peer collaboration or cooperative learning helps

students’ understanding of issues/concepts.

Having students write reflectively every day to reiterate

and consolidate learning.

Using simulations to involve students in understanding

various points of view.

Adding it Up – Report of the

National Research Council

Five intertwining strands

constitutes mathematical proficiency

1) Conceptual understanding

2) Procedural fluency

3) Strategic competence

4) Adaptive reasoning

5) Productive disposition

Mathematical Proficiency: The Five Strands

Reasoning

Problem

Solving/Application

Conceptual Understanding

Mathematical Confidence

Knowledge of Procedures

Adding It Up Helping Children Learn Mathematics, National Research Council

How Students Learn

Mathematics in the Classroom

National Research Council

Contributions from Researchers with

extensive experience in teaching or

partnering with teachers

Research focused on how to promote sense

making, understanding and reasoning in the

math classroom

Conclusions

• Math is not only about learning to compute.

Mathematics is about problem solving and

using computation as a tool for use to that end

when it is helpful.

• If mathematics learning is not grounded in

understanding and does not build on a

student’s own reasoning and strategy

development, then solving problems

successfully will depend on the ability to recall

memorized rules.

Recommendations

Allow students to use their own informal

problem-solving strategies, at least initially, and

then guide their mathematical thinking toward

more effective strategies.

Encourage math talk to clarify their strategies to

themselves and others.

Provide instruction that supports problem

solving, reasoning and metacognition.

National Council of Teachers of

Mathematics

Learning math with understanding is essential.

One of the most robust findings of research is that

conceptual understanding is an important component of

proficiency, along with factual knowledge and procedural

facility (Bransford, Brown, and Cocking 1999).

Students who memorize facts or procedures without

understanding often are not sure when or how to use

what they know, and such learning is often quite fragile

(Bransford, Brown, and Cocking 1999).

• Learning with understanding also makes

subsequent learning easier. Mathematics makes

more sense and is easier to remember and to

apply when students connect new knowledge to

existing knowledge in meaningful ways

(Schoenfeld 1988).

• Well-connected, conceptually grounded ideas are

more readily accessed for use in new situations.

(Skemp 1976).

NCTM – The Teaching Principle

Provide engaging worthwhile math

tasks that promote sense making,

reasoning, application and

mathematical communication so

students develop the understanding

that is essential in learning math.

Additional Sources

http://www.bestevidence.org/math/mhs/mhs_math.htm

http://www.centeroninstruction.org/topic.cfm?k=M

http://dww.ed.gov/

http://dww.ed.gov/media/MathScience/MPR/CI/Learn/flashoverview/index.htm

http://ies.ed.gov/ncee/wwc/

http://www.cpm.org/pdfs/statistics/sallee_research.pdf

http://www.bestevidence.org/math/mhs/mhs_math.htm

http://www.centeroninstruction.org/topic.cfm?k=M

http://dww.ed.gov/

http://dww.ed.gov/media/MathScience/MPR/CI/Learn/flashoverview/index.htm

http://ies.ed.gov/ncee/wwc/

https://mail.lmsd.org/owa/redir.aspx?C=b551b0a650d640f7b8c33c6a1722bc69&URL=http://www.cpm.org/pdfs/statistics/sallee_research.pdf

Lower Merion High School

Grade 8 PSSA data as compared to Grade 11

4-Sight data 2011

*Data reflective of Algebra 1, Geometry CP and Algebra 2 CP students

Grade 8 PSSA 2007-08 85.54% - Proficient and Advanced

Below Basic – 2.41%

Basic – 12.05%

Proficient – 50.60%

Advanced – 34.94%

Grade 11 4-Sight 2010-11 67.47% - Proficient and Advanced


Basic – 26.51%


Advanced – 6.02%


Grade 8 PPSA data as compared to Grade 11

4-Sight data



4-Sight data 2011– African American

*Data reflective of Algebra 1.Geometry CP and Algebra 2 CP students


Below Basic – 10.53% 2 students

Basic – 15.79% 3 students

Proficient – 63.16% 12 students

Advanced – 10.53% 2 students


Below Basic –4.35% 1 student

Basic – 34.78% 7 students


Advanced – 8.70% 2 students



4-Sight data – African American

Harriton High School


4-Sight data 2011

*Data reflective of students who took Algebra 1 CPM, Geometry CPM and Algebra 2 CPM



Basic – 9.38%


Advanced – 12.50%



Basic – 7.32%


Advanced – 14.63%



4-Sight data



4-Sight data 2011 – African American

*Data reflective of students who took Algebra 1 CPM,

Geometry CPM, Algebra 2CPM

Grade 8 PSSA 2007-08 100% - Proficient and Advanced


Advanced – 42.96% 1 student


Below Basic – 12.50% 1 student




4-Sight data – African American

Harriton High School C or Better Report

First Quarter

84

93 90

75

91

79

0

10

20

30

40

50

60

70

80

90

100

Algebra 1 Geometry Algebra 2

ALL

AFRICAN AMERICAN

Lower Merion High School C or Better Report

First Quarter

8682 81

77

65 64

0

10

20

30

40

50

60

70

80

90

100


ALL

AFRICAN AMERICAN

Bala Cynwyd D and F Report

Comparison

This year Last year

All African

American

All African

American

Math 6 4 1 1 0

Pre-Algebra 0 0 4 2

Intro to Algebra 3 2 5 2

Total 7 3 10 4

Welsh Valley D and F report

Comparison

This Year Last Year

All African

American

All African

American

Math 6 5 2 1 0

Pre- Algebra 5 1 10 4

Intro to Algebra 11 4 7 3

Total 21 7 18 7

Where are we going?

Grades 6 to 8 Implementation of CPM in Algebra 1 –2011/12 (one-year course for

many) Administration of benchmark exams that assess not only skills but

understandings as well. Analyze data from PSSA and benchmarks to assess effectiveness of

curriculum and the core math resource Continued professional development and collaboration opportunities

with High School and Elementary teachers Implementation of pre and post attitude survey for students Continue to provide support to students through additional math

classes (e.g. excel) and after school sessions with a targeted focus on areas of need as evidenced in the PSSA

Monitor student progress using on-going assessment, 4-Sight, teacher and district made assessments as well as PSSA

Grades 9 to 12 (2011-2013) Implementation of CPM to support District curriculum in all College Prep

courses

Common benchmark assessments that assess not only skills but understanding as well

Continued articulation opportunities across grade levels and courses (planning, collaborative scoring, looking at student work; data analysis etc…)

Analyze data from 4- Sight, PSSA and benchmarks to assess effectiveness of curriculum and the core math resource being used to support it

Continue to provide support to students through the math labs, with a targeted focus on areas of need as evidenced in the PSSA

Possibly provide additional before and after school opportunities for students to receive support and monitor their progress using on-going assessment, 4-Sight, teacher and district made assessments as well as PSSA

MATH SEQUENCE K-12

Prior Math Sequence

GR 4 GR 5 GR 6 GR 7 GR 8 GR 9 GR 10 GR 11 GR 12

Test

ing:

ER

B, C

BA

, Per

form

ance

Crit

eria

, Gra

des

Pre-Algebra

2 years above

grade level

Intro to

Algebra


H

Math

Analysis /

Trig H

Calculus

AB or BC

or AP

Statistics

Senior

Seminar or

Calculus

AB or BC

or AP Stat

Accelerated

Math

1 year above

grade level

(Math 6)

Pre-

Algebra

Intro to

Algebra

Algebra 1 Geometry

H

Algebra 2

H

Math

Analysis /

Trig H

Calculus

AB or BC

or AP

Statistics

*Math 5

(testing at end

of year for

possible

acceleration to

Pre-Algebra)

Math 6 Pre-

Algebra

Intro to

Algebra

Algebra 1 Geometry Algebra 2 Math

Analysis /

Trig or

Algebra 3

Trig or

Statistics

Rationale for Change

• To provide a meaningful and challenging math

experience for all students.

• To provide to all students a strong foundation

and understanding of key mathematical

concepts necessary for success in Algebra 1

and beyond.

• To offer the opportunity for students to take

Algebra 1 in one year as opposed to two.

• To provide an additional opportunity for

students on grade level at the middle level to

advance.

Proposed Math Sequence For 2010/112009/10 2010/11 2011/12 2012/13 2013/14 2014/15 2015/16 2016/17 2017/18

GR 4 GR 5 GR 6 GR 7 GR 8 GR 9 GR 10 GR 11 GR 12Te

stin

g:E

RB

, CB

A, P

erfo

rman

ce C

riter

ia, G

rade

s

Accel-

erated

Math

(Math 6)

Pre-

Algebra

Algebra 1

Intro to

Algebra

Geometry

Algebra 1

Algebra 2

H

Geometry

(H)

Math

Analysis

/Trig H

Algebra

2(H)

Calculus

AB or BC

or AP Stat

Math

Analysis/

Trig (H ) or

(AP)

Statistics

Senior

Seminar or

Calc AB or

BC or AP

Stat

Calculus

CP; AB or

BC or (AP)

Statistics

Math 5 Math 6 Pre-Algebra

*Testing for

possible

placement

into a one

year

Algebra 1

course

Algebra 1

Intro to

Algebra

Geometry

(H)

Algebra 1

Algebra 2

(H)

Geometry

Math

Analysis/

Trig (H ) or

(AP)

Statistics

Algebra 2

Calculus AB

or BC or

(AP)

Statistics

(AP) Stat or

Math

Analysis /

Trig or

Algebra 3

Trig

GR 6 GR 7 GR 8 GR 9 GR 10 GR 11 GR 12

Intro to

Algebra


H

Math

Analysis /

Trig H

Calculus

AB or BC

or AP

Statistics

Senior Seminar

or Calculus AB

or BC or AP

Stat

Pre-

Algebra

*Testing for

possible

placement

into a 0ne-

year

Algebra 1

course

Intro to

Algebra

Algebra 1

Algebra 1

Geometry

Geometry

H

Algebra 2

(H)

Algebra 2

H

Math

Analysis /

Trig (H) or

(AP) Stat

Math

Analysis /

Trig (H) or

(AP) Stat

Calculus

CP, AB or

BC or ( AP)

Statistics

Calculus CP,

AB or BC or

((AP) Statistics

Senior Seminar

or Calculus AB

or BC or AP

Stat

Math 6 Pre-

Algebra

Testing for

possible

placement

into a 0ne-

year

Algebra 1

course

Intro to

Algebra

Algebra 1

Algebra 1

Geometry

(H)

Geometry

Algebra 2

(H)

Algebra 2

Math

Analysis /

Trig (H) or

(AP) Stat

Math Analysis /

Trig or Algebra

3 Trig or

Statistics

Calculus CP,

AB or BC or

((AP) Statistics

GR 7 GR 8 GR 9 GR 10 GR 11 GR 12


H

Math

Analysis /

Trig H

Calculus AB

or BC or AP

Statistics

Senior Seminar or

Calculus AB or BC or AP

Stat

Intro to

Algebra

Algebra 1 Geometry

(H)

Algebra 2

(H)

Math Analysis

/ Trig (H) or

(AP) Stat

Calculus CP, AB or BC

or (AP) Statistics

Pre-

Algebra

Testing for

possible

placement

into a 0ne-

year

Algebra 1

course

Intro to

Algebra

Algebra 1

Algebra 1

Geometry

(H)

Geometry

Algebra 2

(H)

Algebra 2

Math Analysis

/ Trig (H) or

(AP) Stat

Math Analysis / Trig or

Algebra 3 Trig or (AP)

Statistics

Calculus CP, AB or BC

or (AP) Statistics

Questions and FeedbackThank you

Secondary Mathematics · Merion School District math curriculum –it is not our curriculum. •...

Documents

Transcript of Secondary Mathematics · Merion School District math curriculum –it is not our curriculum. •...