Using license plates as a context, we will analyze patterns. I will share a technique for graphing, and you will design your own license plates with given parameters. Our graphs will offer entry into transformational geometry, and a mapping from letters to numbers allows us to experience early algebra in context.

License plates are a useful context to work with numbers, and in this article you will see a range of activities in which to engage your students. Some innovative graphing concepts are presented with license plates that allow students to investigate transformations including translations, reflections, and rotations.

Using license plates as a context, we will analyze patterns. I will share a technique for graphing, and you will design your own license plates with given parameters. Our graphs will offer entry into transformational geometry, and a mapping from letters to numbers allows us to experience early algebra in context.

Using license plates as a context, we will analyze patterns. I will share a technique for graphing, and you will design your own license plates with given parameters. Our graphs will offer entry into transformational geometry, and a mapping from letters to numbers allows us to experience early algebra in context.

Using license plates as a context, we will analyze patterns. I will share a technique for graphing, and you will design your own license plates with given parameters. Our graphs will offer entry into transformational geometry, and a mapping from letters to numbers allows us to experience early algebra in context.

The concept of function is one of the essential topics in the teaching and learning of secondary mathematics because of the central and unifying role it plays within secondary and college level mathematics. Organizations, such as the National Council of Teachers of Mathematics, suggest students should be able to make connections across multiple representations of mathematical functions by the time they complete high school. Despite the prominent role functions play in secondary mathematics curriculum, students continue to struggle with the complex notion of functions and especially have difficulty using the different representations that are inherent to functions (algebraic, graphical and tabular). Technology is often considered an effective tool in raising student achievement, especially in learning functions where the different representations of a graphing calculator are analogous to the different representations of a function. Opportunity to learn is another important consideration when examining achievement and is generally considered one of, if not the most important, factor in student achievement. Opportunity to learn, or the measure of to what extent students have had an opportunity to learn or review a concept, is often measured with self-reports of content coverage. This study examined the relationship between opportunity to learn, students'; use of graphing calculators, and achievement within a curriculum that supports integrated use of technology and focuses on conceptual understanding of mathematical concepts. The research questions focused on what opportunities students had to learn functions from the enacted curriculum, what calculator strategies students used when solving function problems, how both opportunity to learn and calculator strategies influenced student achievement, and what relationships exist between opportunity to learn, use of calculator strategies, and student achievement. This study is an in-depth secondary analysis of a portion of data collected as part of the evaluation study of Precalculus and Discrete Mathematics (Third Edition, Field-Trial Version) developed by the University of Chicago School Mathematics Project. Participants in this study (n = 271) came from six schools, seven teachers, and 14 classes. Instruments in this study include two pretests (one with technology and one without) and three posttests (two with technology and one without) and a calculator usage survey for one posttest. In addition to five student assessments, teachers completed opportunity-to-learn surveys for the posttests and chapter evaluations forms on which they indicated the lessons taught and the homework problems assigned from the textbook. Some students (n = 151) had access to graphing calculators equipped with computer algebra systems (CAS) while others (n = 120) had access to graphing calculators. Students had multiple opportunities to learn functions as measured by lessons taught, homework assigned, and posttest items teachers reported as having taught or reviewed the content necessary for students to correctly answer the items. Overall, students showed a positive increase in achievement between the pretests and posttests. In general, achievement was positively correlated to OTL Lessons, negatively correlated to OTL Homework, and had no correlation to OTL Posttests when controlling for prior knowledge. Results indicate students appear to be, for the most part, making wise choices about when and how to use graphing calculators to solve function items. Students prefer the graphical representation and are rarely using CAS features or tables, even when they are the best choices for solving a problem. Results from hierarchical linear models (HLM) show use of strategies (beta = 0.96), access to CAS (beta = 5.12), and OTL lessons (beta = 0.75) all had significant and positive impacts on student achievement for one of the posttests, when controlling for prior knowledge. Results from path analyses also indicated use of strategies had a direct and positive effect (beta =0 .14) on student achievement but showed access to CAS had a negative indirect effect (beta = -0.64) on student achievement for the same posttest mitigated through OTL Lessons (beta = 0.30). The results of this study have implications for both researchers and mathematics educators who seek to understand ways in which teachers can increase students'; understanding of functions and student achievement. The relationship between the use of technology and student achievement in relation to opportunity to learn is complex, but use of calculator strategies appears to have a positive effect on students' opportunity to learn functions and student achievement when used in a curriculum that focuses on conceptual understanding and integrates technology.

Mathematics education could and should benefit from technology in order to improve teaching and learning, particularly in topics where visualizations and connections to other concepts are needed. Handheld technologies such as graphing calculators can provide students with visualization, confirmation and exploration of problems and concepts they are learning. Handheld graphing technologies have been taken place widely in elementary and secondary level mathematics courses and considered to be beneficial in various means in mathematics education. Mathematics teachers have a crucial role in the use of GCs in mathematics classrooms. Therefore, pre-service teachers&rsquo / use of GCs and their views on the use of the tool in mathematics learning are considered to be valuable. The purpose of this study was to investigate the difficulties pre-service elementary mathematics teachers face, and the benefits and constraints they emphasize while learning elementary school algebra through using the Casio Classpad after receiving an instruction with graphing calculators. The graphing calculator used in the present study is the Casio Classpad 330, which is an evolved handheld device combining features of graphing calculators, dynamic geometry environment, computer algebra systems and more. The following two research problems guided the study: What are the difficulties do pre-service elementary mathematics teachers face while using Classpad in learning elementary school algebra after receiving an instruction with graphing calculators? What benefits and constraints do pre-service elementary mathematics teachers emphasize while learning elementary school algebra through using Classpad after receiving an instruction with graphing calculators? With the aim of investigating the views of a group of pre-service elementary mathematics teachers, qualitative research strategies were used. The data was collected and analyzed by means of a case study design. Classroom observations, a questionnaire, and focus group interviews were the main data sources of the existing study. The study was carried out with 21 pre-service elementary mathematics teachers. In the classroom studies elementary level algebra was taught to the participants with the use of Classpad as a main tool by giving one tool to each of the participants. Classroom observations ended in five weeks &ndash / 20 courses &ndash / including one week of a training period. After the classroom observations, participants filled out a questionnaire including five open-ended questions about the classroom studies. Finally, data collection procedure was ended with three focus group interviews. The data was analyzed with qualitative means by transcribing and analyzing the observation records, answers of the questionnaire, and records of the three interviews. Results revealed that pre-service teachers&rsquo / view Classpad in three categories / as a personal tool, as an educational tool, and the relationship between CP and motivation. They viewed CP as a personal tool that they were eager to use the tool in every level of mathematics from elementary to mastering degrees. As an educational tool, they preferred to use the tool as a teacher by giving some cautions that teachers and students should be careful with. Lastly, they considered that the tool has a positive effect on motivation when used appropriately. Pre-service elementary mathematics teachers faced some difficulties in the beginning courses of the classroom studies which was their learning period of how to use CP and they overcome most of the difficulties at the end of the classroom studies. As the new elementary school level mathematics curriculum encourages the use of various technologies in teaching and learning of mathematics, the results of this study will have useful implications for mathematics teachers and curriculum developers.

The purpose of this study was to advance knowledge about the relationship between graphing calculator use and classroom norm development. An interpretive case study design incorporating qualitative and quantitative research methods was used to explore the question: What happens when an exemplary teacher uses graphing calculators in a college algebra class? The purposively selected participants were the teacher and eleven students of a Texas community college algebra course. All 29 classes of the 14-week spring 2006 semester were observed in their entirety by the researcher. The theoretical frameworks guiding the study were the affective representation system and the Multiple Representations Model of Learning and Teaching with the use of the Mathematics and Science Classroom Observation System for data collection, analysis, and profiling of classroom lessons. Originally developed for grades K-12, the use of the instrument was extended to college algebra. Triangulation of data sources using constant comparative and content analysis methods were used to support the three major findings: (1) The instructor's proactive orchestration of specialized instruction, support materials, and designed activities contributed to the establishment of graphing calculator use as an essential part of classroom norms and promoted students' independent use of the tool; (2) The dynamic and interactive features of the TI-84 Plus graphing calculator facilitated the delivery of instruction at high cognitive levels during student interactive activities providing access to, exploration of, and use of multiple representations for some mathematical concepts and solutions not easily attainable using traditional methods; and (3) Although the majority of students had never used a graphing calculator before the course, all students used the tool at appropriate times during instructional activities, self-reporting that their use of the calculator was generally beneficial for enhancing their understanding of lessons and supporting class interactions. Additionally, all students independently chose to use the calculator during major assessments and reported knowledgeable use of the tool to facilitate improved test performance. Replication of the study is limited because the norms developed in this case are unique to the teacher and students who negotiated their establishment. Suggestions are given regarding educational policies, reform practices, and research extensions.

This dissertation consists of four articles and a summary. The main focus of the studies is students' explorations in upper secondary school mathematics. In the first study the central research question was to find out if the students could learn something difficult by using the graphing calculator. The students were working with questions connected to factorisation of quadratic polynomials, and the factor theorem. The results indicate that the students got a better understanding for the factor theorem, and for the connection between graphical and algebraical representations. The second study focused on a the last part of an investigation, the verification of an idea or a conjecture. Students were given three conjectures and asked to decide if they were true or false, and also to explain why the conjectures were true or false. In this study I found that the students wanted to use rather abstract mathematics in order to verify the conjectures. Since the results from the second study disagreed with other research in similar situations, I wanted to see what Swedish teachers had to say of the students' ways to verify the conjectures. The third study is an interview study where some teachers were asked what expectations they had on students who were supposed to verify the three conjectures from the second study. The teachers were also confronted with examples from my second study, and asked to comment on how the students performed. The results indicate that teachers tend to underestimate students' mathematical reasoning. A central focus to all my three studies is explorations in mathematics. My fourth study, a revised version of a pilot study performed 1998, concerns exactly that: how students in upper secondary school explore a mathematical concept. The results indicate that the students are able to perform explorations in mathematics, and that the graphing calculator has a potential as a pedagogical aid, it can be a support for the students' mathematical reasoning.

This study was designed to investigate the roles of gender and learning styles on tenth grade students&amp / #8217 / kinematics graphing skills. The study was conducted in 14 representative cities throughout seven different geographical regions over Turkey with a total of 989 tenth grade students in last four weeks of the spring semester of 2002-2003 school year. Findings of the kinematics graphing skills test indicated that general performances of the students were very low and many students have difficulties in interpreting kinematics graphs. When the data were analyzed using Analysis of Covariance (ANCOVA), while controlling the effects of students&amp / #8217 / age, previous physics course grades and previous mathematics course grades, the results indicate that there was no significant difference among the kinematics graphing skills test scores of students having different learning styles. Similarly, no significant difference was found between the kinematics graphing skills test scores of female and male students. However, a significant interaction was observed between gender and learning styles on students&amp / #8217 / kinematics graphing skills test scores. The most common learning style type was assimilator for the participants of this study. Accommodator female students&amp / #8217 / kinematics graphing skills test scores were higher than that of female students having other learning styles and converger male students&amp / #8217 / kinematics graphing skills test scores were higher than that of male students having other learning styles on kinematics graphing skills test. Bivariate correlations revealed significant positive correlations between students previous physics course grades, previous mathematics course grades, and age and their kinematics graphing skills test scores.