“Becoming proficient with whole numbers is more complicated than many people realize. It is not simply moving from ignorance to competence. Nor is it a matter of students following the teachers’ directions and explanations and then practicing until they get it right. Rather, it involves students- with the support from learning materials, teachers, and peers- inventing, understanding, and practicing methods; trying to learn and use concepts that look easy to adults but are challenging for children (e.g., place value); and gradually increasing their mathematical proficiency by continually seeking to make sense of number and numerical operations.” (National Research Council, 2001)

Wright Group/ McGraw Hill
Copyright 2004
Cost- $1000 per grade www.gwmath.com

Brief Description

Growing With Mathematics is a program designed for students grades kindergarten through sixth. The program is designed to teach problem solving approaches to learning mathematics. Students explore math through hands on activities which allow them to construct their own knowledge of the subject matter. Students also practice computation skills through many different approaches such as connecting mathematics to real life applications. The program is focused on number sense which is derived through literacy skills such as oral and written communication to help build understanding of mathematics concepts. This program is effective for students with mild/moderate disabilities because it is student centered and requires peers to work collaboratively. Also, teachers are provided with extensions and adaptations ensuring that all students’ needs are met.

Analysis of Program

“Becoming proficient with whole numbers is more complicated than many people realize. It is not simply moving from ignorance to competence. Nor is it a matter of students following the teachers’ directions and explanations and then practicing until they get it right. Rather, it involves students- with the support from learning materials, teachers, and peers- inventing, understanding, and practicing methods; trying to learn and use concepts that look easy to adults but are challenging for children (e.g., place value); and gradually increasing their mathematical proficiency by continually seeking to make sense of number and numerical operations.” (National Research Council, 2001)

Growing with Mathematics is a research based program that comes from cognitive psychology, sociocultural theories, and mathematics education. The research found that the content is organized into five learning areas. The research findings suggest:
1. There is an emphasis on place value and number sense (Cobb and Wheatley, 1988; Fusion et al., 1997).
2. The use of thinking strategies for promoting mastery of addition and subtraction facts (Thorton, 1990; Issacs and Carroll, 1999).
3. The use of patterns and relationships to develop understanding of multiplication (Armstrong, B. E., N. B. Vacc, 1995).
4. The use of models of situations involving multiplication and division (Greer, F., 1992).
5. The development of multiplicative reasoning (Harel, G.& Confrey, J., 1994; Steffe, L., 1994).
6. The relationship between conceptual and procedural knowledge in learning , mathematics (Rittle-Johnson, B.& Siegler R.S., 1998).

Integration of Math Skills

In Growing with Mathematics, language development is “modeled as a spiral” (Growing with Mathematics Overview, 0-4). Students use everyday language in their problem solving experiences. They are presented with real world problems which connect mathematics with language. Children’s written and verbal language becomes more coherent through the opportunities to communicate their mathematical ideas

Instruction

Skills are taught in a developmental progression. Students are first introduced to a concept on a concrete level and are built upon until they have reached the abstract level. This program takes a student centered approach and uses multi-sensory instruction through tactile learning opportunities. Growing With Mathematics is not based on practice and learning (drilling) but rather exploration and discovery. Students are encouraged to create their own approaches in problem solving to develop problem solving strategies. This program is used not only with individual learners but as a general education curriculum derived from The Principles and Standards for School Mathematics (NCTM, 2000). A standard lesson would begin with a daily number sense starter, followed by a brief background of the concept, an investigation (whole group, small group, or paired), discussion and finally an assessment.

Assessment

Growing with Mathematics has three styles of assessment; teacher, student, and on-going. There are two types of teacher assessment. First, the teacher observes students’ understanding through their discussions and explorations. Second, there is a formal assessment at the end of every topic that includes a multiple choice practice test, a check up, and a performance task with a scoring rubric. The students reflect and assess their own responses on questions posed by the teacher. The ongoing assessment is done through their daily understanding and a student made portfolio that keeps all of students’ work for teachers and parents to evaluate.

Texts and Materials

-student discussion book
-student soft cover workbook
-resource kit
-real world math books
-manipulative kit

Training Requirements

Teachers must undergo an extensive training and practice in administering lessons based on Growing with Mathematics. It is a program that is very modern in its approach to teaching mathematics because it is student centered and not teacher driven. Teachers need to learn ways to prompt their students for exploration instead of modeling and having students practice until they have reached proficiency.

Inclusive Classroom

Growing with Mathematics is ideal for an inclusive classroom because it involves students working together to develop strategies for problem solving. Students are taught to develop strategies in a variety of ways including manipulatives and trial and error.

Strengths

Teachers have structure and organization throughout their lessons. Students work in collaborative groups which foster social skills and development for all students regardless of learner needs. Students are given a variety of ways to solve problems encouraging students to use their own individual strengths. Growing with Mathematics is language based taking an interdisciplinary approach to mathematics. This program also emphasizes a variety of useful assessments which enable the teacher to monitor student progress making sure everyone is succeeding.

Weaknesses

This program is very language based which makes it difficult for English Language Learners (ELL) and students with language impairments. Many teachers specifically including a 4th-6th grade self contained teacher stated, “This program is difficult for my students because it is language based and most of my students have reading and writing needs which makes it difficult for them to understand the way the concepts are presented”.
According to a report on Growing with Mathematics by educator Calvin Irons, there are many weaknesses to this program. He writes about mathematical issues, students with special needs and their problems with this program as well as end of year test results.
Refer to the following article regarding Irons' article: http://carolynwright.org/GWM/JarvisGWM.pdf

Final Reflection
After extensively reviewing Growing with Mathematics we would not use this program in a Special Education self contained classrooms. Students in a special education self contained classroom would need more scaffolding and guidance because of the more severe disabilities in the classroom. We believe that students in this setting need more practice to learn functional skills which they can apply in everyday life. They must learn algorithms and how they work without having to try to figure out a strategy themselves. Also, a language based program is not the most effective way to teach students in a Special Education classroom mathematics because it teaches more than one discipline at the same time, risking confusion in one subject based on deficiencies in another.
However, this program could be successfully used in an inclusive classroom. Working in collaborative groups provides students the opportunity to teach each other in ways that make sense to them at their own cognitive level. Students can benefit from working with their peers who are more advanced learning because of their prior experiences. All students in these collaborative groups can use their strengths to assist each other in the exploration of the topic. The program helps prepare students for real life situations through problems that apply to everyday life.

Britta VenterBelinda McGehee

Michael Redmon

Growing With Mathematics“

Becoming proficient with whole numbers is more complicated than many people realize. It is not simply moving from ignorance to competence. Nor is it a matter of students following the teachers’ directions and explanations and then practicing until they get it right. Rather, it involves students- with the support from learning materials, teachers, and peers- inventing, understanding, and practicing methods; trying to learn and use concepts that look easy to adults but are challenging for children (e.g., place value); and gradually increasing their mathematical proficiency by continually seeking to make sense of number and numerical operations.” (National Research Council, 2001)Wright Group/ McGraw Hill

Copyright 2004

Cost- $1000 per grade

www.gwmath.com

Brief DescriptionGrowing With Mathematics is a program designed for students grades kindergarten through sixth. The program is designed to teach problem solving approaches to learning mathematics. Students explore math through hands on activities which allow them to construct their own knowledge of the subject matter. Students also practice computation skills through many different approaches such as connecting mathematics to real life applications. The program is focused on number sense which is derived through literacy skills such as oral and written communication to help build understanding of mathematics concepts. This program is effective for students with mild/moderate disabilities because it is student centered and requires peers to work collaboratively. Also, teachers are provided with extensions and adaptations ensuring that all students’ needs are met.

Analysis of Program“Becoming proficient with whole numbers is more complicated than many people realize. It is not simply moving from ignorance to competence. Nor is it a matter of students following the teachers’ directions and explanations and then practicing until they get it right. Rather, it involves students- with the support from learning materials, teachers, and peers- inventing, understanding, and practicing methods; trying to learn and use concepts that look easy to adults but are challenging for children (e.g., place value); and gradually increasing their mathematical proficiency by continually seeking to make sense of number and numerical operations.” (National Research Council, 2001)

Growing with Mathematics is a research based program that comes from cognitive psychology, sociocultural theories, and mathematics education. The research found that the content is organized into five learning areas. The research findings suggest:

1. There is an emphasis on place value and number sense (Cobb and Wheatley, 1988; Fusion et al., 1997).

2. The use of thinking strategies for promoting mastery of addition and subtraction facts (Thorton, 1990; Issacs and Carroll, 1999).

3. The use of patterns and relationships to develop understanding of multiplication (Armstrong, B. E., N. B. Vacc, 1995).

4. The use of models of situations involving multiplication and division (Greer, F., 1992).

5. The development of multiplicative reasoning (Harel, G.& Confrey, J., 1994; Steffe, L., 1994).

6. The relationship between conceptual and procedural knowledge in learning , mathematics (Rittle-Johnson, B.& Siegler R.S., 1998).

Integration of Math SkillsIn Growing with Mathematics, language development is “modeled as a spiral” (Growing with Mathematics Overview, 0-4). Students use everyday language in their problem solving experiences. They are presented with real world problems which connect mathematics with language. Children’s written and verbal language becomes more coherent through the opportunities to communicate their mathematical ideas

InstructionSkills are taught in a developmental progression. Students are first introduced to a concept on a concrete level and are built upon until they have reached the abstract level. This program takes a student centered approach and uses multi-sensory instruction through tactile learning opportunities. Growing With Mathematics is not based on practice and learning (drilling) but rather exploration and discovery. Students are encouraged to create their own approaches in problem solving to develop problem solving strategies. This program is used not only with individual learners but as a general education curriculum derived from The Principles and Standards for School Mathematics (NCTM, 2000). A standard lesson would begin with a daily number sense starter, followed by a brief background of the concept, an investigation (whole group, small group, or paired), discussion and finally an assessment.

AssessmentGrowing with Mathematics has three styles of assessment; teacher, student, and on-going. There are two types of teacher assessment. First, the teacher observes students’ understanding through their discussions and explorations. Second, there is a formal assessment at the end of every topic that includes a multiple choice practice test, a check up, and a performance task with a scoring rubric. The students reflect and assess their own responses on questions posed by the teacher. The ongoing assessment is done through their daily understanding and a student made portfolio that keeps all of students’ work for teachers and parents to evaluate.

Texts and Materials-student discussion book

-student soft cover workbook

-resource kit

-real world math books

-manipulative kit

Training RequirementsTeachers must undergo an extensive training and practice in administering lessons based on Growing with Mathematics. It is a program that is very modern in its approach to teaching mathematics because it is student centered and not teacher driven. Teachers need to learn ways to prompt their students for exploration instead of modeling and having students practice until they have reached proficiency.

Inclusive ClassroomGrowing with Mathematics is ideal for an inclusive classroom because it involves students working together to develop strategies for problem solving. Students are taught to develop strategies in a variety of ways including manipulatives and trial and error.

StrengthsTeachers have structure and organization throughout their lessons. Students work in collaborative groups which foster social skills and development for all students regardless of learner needs. Students are given a variety of ways to solve problems encouraging students to use their own individual strengths. Growing with Mathematics is language based taking an interdisciplinary approach to mathematics. This program also emphasizes a variety of useful assessments which enable the teacher to monitor student progress making sure everyone is succeeding.

WeaknessesThis program is very language based which makes it difficult for English Language Learners (ELL) and students with language impairments. Many teachers specifically including a 4th-6th grade self contained teacher stated, “

This program is difficult for my students because it is language based and most of my students have reading and writing needs which makes it difficult for them to understand the way the concepts are presented”.According to a report on Growing with Mathematics by educator Calvin Irons, there are many weaknesses to this program. He writes about mathematical issues, students with special needs and their problems with this program as well as end of year test results.

Refer to the following article regarding Irons' article:

http://carolynwright.org/GWM/JarvisGWM.pdf

Final ReflectionAfter extensively reviewing Growing with Mathematics we would not use this program in a Special Education self contained classrooms. Students in a special education self contained classroom would need more scaffolding and guidance because of the more severe disabilities in the classroom. We believe that students in this setting need more practice to learn functional skills which they can apply in everyday life. They must learn algorithms and how they work without having to try to figure out a strategy themselves. Also, a language based program is not the most effective way to teach students in a Special Education classroom mathematics because it teaches more than one discipline at the same time, risking confusion in one subject based on deficiencies in another.

However, this program could be successfully used in an inclusive classroom. Working in collaborative groups provides students the opportunity to teach each other in ways that make sense to them at their own cognitive level. Students can benefit from working with their peers who are more advanced learning because of their prior experiences. All students in these collaborative groups can use their strengths to assist each other in the exploration of the topic. The program helps prepare students for real life situations through problems that apply to everyday life.

Sources:

Growing With Mathmatics Overview- book

www.ed.gov

www.wrightgroup.com

http://carolynwright.org/GWM/JarvisGWM.pdf- article