Manipulatives

1. How do you hold every student accountable when using manipulatives for an activity?

I think that it is important that each student is held accountable when using manipulatives for an activity. It is important that the teacher assess each students' knowledge and ability to apply knowledge of a concept through manipulatives. One way that each student could be held accountable when using manipulatives for an activity is to have them each student record their thought process when using manipulatives in their math journal/notebook. This allows the teacher to individually assess each students' knowledge of a topic through the use of manipulatives. The activity we used in class was a great way to hold the students accountable. We each had to record the various activities and we had to work together to create the various activities that each type of manipulative could be used for.

2. Why do people say "hands-on, minds-on," instead of just "hands-on"?

Hands-on, minds-on is referring to the use of manipulatives. When students are using manipulatives they are engaging the mind by using and manipulating different objects to strengthen and build of different math knowledge and concepts. Students' brains are engaged in the manipulatives that they are using and as a result they are stimulating their minds. Manipulative use in the classroom allows the students to apply their knowledge in a way of "doing." When students physically manipulate objects they are applying their knowledge of various mathematical concepts to real-life situations, and they are able to physically see the process of how some math concepts and carried out. When manipulatives are used correctly, paralleled with strong and effective instruction, they will begin to investigate, explore, and ask various questions about concepts.

3. How do the process standards fit with the manipulative activity?

The process standards relate closely with manipulative work. Students are using problem solving when working with manipulatives when they must find a way to use the manipulatives in a way to solve the given problem or situation. Reasoning and proof is incorporated in manipulative use because the students are using the manipulatives to reason and problem solve to provide proof for their solutions they find. Communication is related to manipulative use when they it is used to express the process of a mathematical concept. Students may also have to use the manipulatives in their justification for a solution that they have found. Connections can be made when students are using manipulatives because they are able to use the objects to help relate to two mathematical concept together with a visual and physical representation. Representation is always applied to manipulative work. Manipulatives are used so that representations can be formed. Manipulatives can be used to represent fractions, sorting, patterns, probability, and many other mathematical concepts.

MTMS - A Framework for Analyzing Geometric Pattern Tasks

Friel, S. N., & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in the Middle School, 15(1), 24-33.

A Framework for Analyzing Geometric Pattern Tasks is an article that discusses how teachers can use geometric patterns to promote the understanding of functional relationships by students. The article focuses on figural reasoning during the process of inductive reasoning. The authors state "when students use figural reasoning, they are able to make sense of patterns, ..., by paying attention to visual cues that can be organized and translated to numeric sequences (Friel & Markworth, 2009). The article was organized into three sections. The first section discussed various problem solving processes that support the use of figural reasoning as a way to explore and interpret geometric pattern tasks and generalize function rules. The second section discussed a framework for distinguishing the complexity of geometric pattern tasks. The framework may be used as applied contexts for figural reasoning. The third section provides a summary of various ways for how the long-term and extended use of geometric pattern tasks contribute to an overall development of students' functional thinking.

I thought that this article was good, but could be confusing at times. There were many instances that I found myself having to go back and re-read multiple sections. I liked that it explained and directly stated how the topic discussed in the article relates to the NCTM Principles and Standards for School Mathematics. I really liked that the there were many examples provided in the article. Having those tables and figures helped apply what was being said in the article with real world student work. I thought that this could be helpful to teachers. Sometimes it is difficult to fully understand how something can be applied to in the classroom. Providing the examples helps teachers have a greater understanding on the techniques explained and discussed. Although I found the tables and figures provided in the article to be very beneficial, there were times when it was very confusing and irritating to flip back and forth between the pages to try and see what was being discussed and referenced in the article. I liked that the authors included a brief paragraph explaining that geometric pattern tasks, although a valuable way to promote figural reasoning and develop a rich conceptual understanding of functions, it has its limitations as well. This information provides teachers with a realistic view of the topic. That realistic view allows teachers to be prepared for the limitations they will reach, and allows them the opportunity to be prepared for dealing with those limitations.