Next Middle School

1. Constance Kamii

a) Brief biography

Dr. Constance Kamii was born in Switzerland, Geneva, where she attended elementary school. She later went to Los Angeles for her high school education and to Pomona College for her college education. She was awarded a Ph.D. in psychology add education from University of Michigan. Today she is professor of early childhood education (ECD) at the Alabama University in Birmingham

b) Major contributions

She has been instrumental in developing of mathematical knowledge in young children, through her theory of Piaget’s theory. She continues to assist young children in understanding the implication of Piagetian theory. Her intellectual sincerity, together with a constant connection between the practice and Piaget’s theory leads a solid input into mathematics education of children.

c) Impact statement

She has made the teaching of mathematics, especially to young children possible. In that, if we work together with children, and lend them our ears, as well as watching them, the understanding of the concepts being thought will be simply. When teaching we ought to be very keen on watching how young children represent their understanding of what is being thought, especially with mathematics.

2. Catherine Twomey Fosnot

a) Brief biography

She is an Education professor at City College in New York City, Mathematics director in the City, and a national center of in- service in the City of New York.

b) Major contribution

Professor Catherine Fosnot has authored a number of articles and books regarding mathematics, the most recent being young mathematicians at work series. Due to her endless effort and significant contribution in developing mathematics, she got teacher of the year award from CCNY in 2005. She also received the ‘young scholar’ award from education communication and technology, as  a director of mathematics in New York city she has twice won the best writing award from AERA’s constructvist.

c) Impact statement

Catherine has positively influenced approaches of teaching, especially Mathematics. She says learning to teach is a developmental process, and you get better in teaching by engaging the kids in investigations, listening to their strategies and ideas and by so doing, you get better in teaching approaches, simply by understanding kids. Teachers should restrain themselves from just teaching their own ideas and strategies.

3. Maarten Dolk

a) Brief biography

He is a developer and researcher of mathematics education in the Netherlands’ Freudenthal Institute.

b) Major contribution

He has developed professional materials for student teachers and teachers, has directed an in- service project in the Netherlands for both staff developers and teacher educators. He is coauthor of young mathematicians at work series.

c) Impact statement

In teaching approaches we need to use, or develop mathematical model for the best interest of the kids. Models are like open number line, and young mathematicians need to ‘own’ and use them in representing their strategies and ideas in problem resolution.

4) Thomas P. Carpenter (Goal oriented behavior theory).

a) Brief biography

He is a professor in the University of Wisconsin Madison, department of curriculum and instruction. He is also a director and researcher of mathematics and science at the national center for improving student learning and achievement in mathematics and Science (NCISLA).

b) Major contribution

He has helped in structuring the early national assessment of education progress (NAEP), he is the one who edited the Journal for research in mathematics education as from 1988 to 1992. He improved student achievements and learning as a director of national center.

c) Impact statement

Young children and other students’ achievement in learning can be positively influenced by the innovative methods of teaching and valid instructions from the teachers. Teachers should incorporate the mathematical ideas of students as part of classroom instructions.

5. Kathy Richardson

a) Brief biography

She received her University education from the Western Washington University from the year 1960 to 1964. She is the owner of math perspectives teacher development center.

b) Major contributions

She has been developing mathematics resource materials for teachers in elementary schools. Kathy’s concept of developing number series is used by both school districts and teachers countrywide. Her mathematical concepts help in assessing young students’ mathematical thinking.

c) Impact statement

When teaching young children, conversations, observations, and less writing should be emphasized, as what children write offers very little of what they think and know.

Cognitively Guided Instruction (CGI)

In this theory you build on the children’s mathematics knowledge, is about the type of the problems, the strategies to take when solving the problem, how the young children develop cognitively, and how the teacher make use of her or his teaching styles. It also avail the framework to the teachers on understanding the computational development of the children.

Problem Centered Learning (PCL)

In this approach of teaching mathematics the tasks or problems are posed to a group of children, and solve the tasks in a collaborative manner. Each group has the mandate of defending its solution ideas to the class. This approach has appeared to spear head the achievement and improved attitude towards mathematics in children.

Conceptually Based Instruction (CBI)

In this kind of approach the students tend to develop the mathematical ideas by simple working through the problem.

Reflection

Teaching the young children to memorize the mathematical concepts, and solving the problems we are not helping the children but killing their mathematical development process. This will further delay the understanding capacity of the children, thus prolonging their ability towards understanding mathematical skills. These theories have also shown that, introducing symbols and equations to elementary children just make them more confused and unable to understand anything. When teaching mathematics we should build on the mathematical knowledge that the children already have, and must know the strategies of solving the math problem making use of all teaching styles that would make the children to understand.

The theories have emphasized working together with children, and ‘lending’ them our ears as well as watching them, the understanding the concepts being thought will be simple. When teaching we ought to be very keen on watching how young children represent their understanding of what is being thought, especially with mathematics. On addition to this, we should pay more attention on observing what children are doing, do a lot of conversations with the children, and give them less of paper work. The logic is that the mathematical ideas and strategies with young children surpass whatever they put down on the papers. We as teacher must put in mind that, a child getting an answer right in a mathematical problem does not automatically mean that he or she understood the underlying mathematical concept. For teacher to prepare young children for tomorrow success in math problems has to make sure children understand the core fundamental concepts of mathematics for success determination in future.

Teachers should encourage the spirit of collaborative learning amongst the children, as this will make them learn further than doing it on a solitary way. This is encouraged by these math theories because talking of children amongst themselves and with the teacher will not only reflect on their thoughts, but generation of thoughts as well. Children’s prior knowledge in math concepts must be recognized and further appreciated by the teacher, and provide logical materials to the children for development of novel mathematical concepts. Creation of community of  learners is an important mathematical program emphasized in these theories, is very essential for young students as they feel  comfortable talking about their errors, understanding other approaches, and working jointly for clear understanding of concepts. A teacher must set up a sense of community, value for others, and conducive surrounding by modeling a upbeat attitude towards math, accepting ‘mistakes’ as openings for learning, nurturing positive significant thinking, generating displays of student mathematics work, and recognizing the exceptional ways in which each child thinks.

Constance Kamii and Kathy Richardson were of a special interest to me, this is because the two encouraged the voice of the learner to be heard in the teaching process. Both put more emphasis on the need to engage the young children in conversations, listening to the children, and appreciating their mathematical concepts. Kathy for instance, put more weight on the teachers making sure that children understand the core foundation of mathematics through observations, conversations, and with less writing, saying that what children write offers very little than what they know and think mathematically (Uab publications, 2005). The questions to pursue as teaching math commences are: How does community learning help young students in understanding math concepts? Which teaching methods to be employed in order math to be developmental and enjoyable for both teachers and children?