THE MAPPING IN THE CONTINUING EDUCATION OF TEACHERS: AN EXPERIENCE THROUGH DISTANCE LEARNING

In this work, we show the experience of continuing teacher education in Cartography in the period from 03/11/2009 to 03/11/2010, it was held by the Center for Continuing Education in Mathematics Education, Science and Environment (CECEMCA) - UNESP - Rio Claro, in DL (Distance Learning). This experience was through the extension course set in TelEduc platform. The course was titled Introduction to Cartography and aimed primarily: Present concepts of systematic and thematic mapping and its potential application in teaching practices, increase knowledge in the areas of Geography, Cartography and Environment; Offer alternatives for implementing content mapping in the classroom.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Sentidos e significados do conceito de divisão provenientes de Atividade Orientadora de Ensino

Pós-graduação em Docência para a Educação Básica - FC

Discourse and Cooperative Learning in the Math Classroom

In this action research study of my 6th grade math classroom I investigated the effects of increased student discourse and cooperative learning on the students’ ability to explain and understand math concepts and problem solving, as well as its effects on their use of vocabulary and written explanations. I also investigated how it affected students’ attitudes. I discovered that increased student discourse and cooperative learning resulted in positive changes in students’ attitudes about their ability to explain and understand math, as well as their actual ability to explain and understand math concepts. Evidence in regard to use of vocabulary and written explanations generally showed little change, but this may have been related to insufficient data. As a result of this research, I plan to continue to use cooperative learning groups and increased student discourse as a teaching practice in all of my math classes. I also plan to include training on cooperative learning strategies as well as more emphasis on vocabulary and writing in my math classroom.

Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

Journal Writing in Mathematics: Exploring the Connections between Math Journals and the Completion of Homework Assignments

In this action research study of sixth grade mathematics, I investigate how the use of written journals facilitates the learning of mathematics for my students. I explore furthermore whether or not these writing journals support students to complete their homework. My analysis reveals that while students do not access their journals daily, when students have the opportunity to write more about one specific problem--such as finding the relationship between the area of two different sized rectangles – they, are nevertheless, more likely to explain their thoughts in-depth and go beyond the traditional basic steps to arrive at a solution. This suggests the value of integrating journal writing in a math curriculum as it can facilitate classroom discussion from the students’ written work.

Cooperative Learning Groups in the Eighth Grade Math Classroom

In this action research study of my classroom of 8th grade mathematics students, I investigated whether cooperative learning would lead to a better understanding of the mathematical concepts and thus more success for the students. I used my three eighth grade classes with two using cooperative groups and the third not. I discovered that the students who wanted to work in cooperative groups were more successful than they had been. I also discovered that the grouping itself has a great effect on how the group works together. The wrong grouping of students can lead to disaster and many headaches for the teacher. Overall the two classes that used cooperative groups did better grade wise than the one class that was taught using the traditional way of not using cooperative groups. As a result of this research, I plan to continue using cooperative groups but will be more aware of the students who are grouped together.

Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom

In this action research of my 6th grade math class, I investigated whether or not my students would improve their ability to reflect on their learning process when they received descriptive feedback from a peer. I discovered the process of giving and receiving feedback was challenging for the students to initially learn, but eventually using the feedback was highly beneficial. Descriptive feedback allowed the students to learn and understand their mistakes immediately, which in turn improved their learning. In my action research, I also began to discover more ways to implement descriptive feedback in my instruction so it could be more effectively for the students and efficiently so there would be less time taken out from instruction. As a result of this research, I plan to continue having students provide and receive descriptive feedback and to find more evidence of how descriptive feedback could influence student achievement.

An Uphill Battle: Incorporating cooperative learning using a largely individualized curriculum

In this action research study of my classroom of 8th grade mathematics, I investigated if cooperative learning could be an effective teaching method with the Saxon curriculum. Saxon curriculum is largely individualized in that most lessons could be completed without much group interaction. I discovered that cooperative learning was very successful with the curriculum as long as it was structured. Ninety-five percent of the students in the study preferred to work in groups, and I observed mathematical communication grow with most of the students. As a result of this research, I plan to continue to incorporate cooperative learning into my mathematics classroom. I will use cooperative learning with all of my mathematics classes, even the ones that do not use the Saxon curriculum. I believe in the power of working together.

Using Cooperative Learning In A Sixth Grade Math Classroom

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of cooperative learning on the engagement, participation, and attitudes of my students. I also investigated the impact of cooperative learning upon my own teaching. I discovered that my students not only preferred to learn in cooperative groups, but that their levels of engagement and participation, their attitudes toward math, and their quality of work all improved greatly. My teaching also changed, and I found that I began to enjoy teaching more. As a result of this research, I plan to continue and expand the amount of cooperative group work that happens in my classroom.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Meaningful Independent Practice in Mathematics

In this action research of my seventh grade mathematics classroom, I investigated how students’ explanations of math homework would improve their learning in math. I discovered these explanations can be very beneficial in helping students to improve their understanding of current skills although it did not affect all students. As a result of this study, I plan to incorporate these student explanations in my instruction next year but not as a daily expectation.

The Importance of Vocabulary Instruction in Everyday Mathematics

In this action research study of my 6th grade math students I try to answer the question of how mathematical vocabulary plays an integral role in the understanding and learning of middle level mathematics. It is my belief that mathematics is a language, and to be fluent in that language one must be able to use and understand vocabulary. With the use of vocabulary quizzes and mathematically-centered vocabulary activities, student scores and understanding of math concepts can be increased. I discovered that many of the students had never been exposed to consistent mathematical terminology in their elementary education, which led many to an unfavorable impression of math. As a result of my research, I plan to incorporate vocabulary as a regular part of my mathematical teaching. As the students understood the language of math, their confidence, attitudes, and scores all began to improve.