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Pre-AP: Topics for AP Vertical Teams® in Math
To succeed in efforts to give students a greater range of mathematics course opportunities, and to increase their awareness about these opportunities while they are still young, high school and middle school teachers must communicate and work with one another. As an AP Vertical Team, a group of mathematics teachers of various grade levels, administrators, and counselors in a school district works cooperatively to develop and implement a vertically aligned program in mathematics.
This one-day workshop focuses on articulating a curriculum anchored in the skills, knowledge, and habits needed for AP mathematics courses. Teachers concentrate on what and how they teach, as well as how they communicate with each other. Teachers will learn the benefits and challenges of vertical teaming and gain an arsenal of activities to use with team members. Some of the section titles include: "What's in It for Me?" "The Least Expensive Cable," "Defining Our Terms," and "What Is the Common Thread?"
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 Pre-AP: Topics for AP Vertical Teams® in Mathematics
Pre-AP: Strategies in Mathematics -- Analyzing and Describing Data
Data is a key component to all of the mathematics and science taught in school today. From the primary counting of objects to multivariable analyses, data forms the basis for most of the problem solving that students see.
This one-day workshop enriches the data analysis topics included in the middle and secondary grades by providing examples of activities where students collect data, use graphs and numerical summaries to get information from data, and communicate that information. Teachers assume the role of students as they discuss data collection and experimental design issues, work through exercises, and share observations and conclusions. Teachers collaborate and share ideas in the workshop just as students will do in class.
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Pre-AP: Strategies in Mathematics -- Analyzing and Describing Data
Pre-AP: Strategies in Mathematics -- Rate
Rate, or rate of change, is a concept that is central to mathematics and mathematical relationships beginning in middle school and continuing throughout high school. Students who aspire to take challenging courses, such as AP Calculus, later in high school and in college must have a strong conceptual understanding of rate. Teachers need to carefully analyze how this concept can be developed throughout the mathematics sequence to allow all students deeper understanding of the associated concepts and applications.
This one-day workshop emphasizes the grade-level-appropriate content, classroom strategies, diagnostic assessment practices, and technology that foster student understanding of rate. Teachers learn highly effective activities to use in the classroom. The focus is on illustrating how content, pedagogy, and embedded assessment can help shape the mathematics curriculum into a seamless strand for students. Specific topics include absolute and relative growth, instantaneous rate, and rate of change.
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Pre-AP: Strategies in Mathematics -- Rate
Pre-AP: Strategies in Mathematics -- Accumulation
Accumulation is a process that has its roots in middle school and early high school mathematics. For example, area and distance are two topics that are often compartmentalized, but are actually related to each other by accumulation. When students have an early introduction and continue to develop their understanding of accumulation at each grade level, they are prepared for challenging classes, such as AP Calculus, later in high school and in college.
In this one-day workshop, teachers examine a seamless development of accumulation concepts for grades 6-12 through grade-level-appropriate content, classroom strategies, and technology usage. Teachers experience and comprehend a guided-exploration approach that they can use in the classroom to build knowledge and further understanding for each student. Teams develop problems, instructional activities, assessment items, and cross-grade lessons for classroom use. Participants learn embedded diagnostic and formative assessment strategies that can be used to develop students' communication skills and allow teachers to monitor and foster mathematical thinking. Specific topics include the concept of area; accumulating distance when speed is constant, changes, or is a function; velocity distinct from speed; and the big picture of accumulation.
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Pre-AP: Strategies in Mathematics -- Accumulation
Pre-AP: Strategies in Mathematics -- Functions
The concept of function is present at almost all levels of school mathematics, from pattern recognition to formal representation and analysis. Function is a key concept that prepares students for success in challenging courses, such as AP Calculus, later in high school and in college.
This one-day workshop allows teachers to develop a deep content knowledge of functions for teachers and discusses grade-level-appropriate content and classroom strategies, including using technology to promote understanding. Teachers will acquire skills that promote methodical thinking and clear communication of thought processes by all of their students. This workshop illustrates a guided-exploration approach as a pedagogical model that emphasizes student thinking as the key to learning and communication as the key to assessing understanding. Specific topics include linear, quadratic, and nonlinear functions.
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Pre-AP: Strategies in Mathematics -- Functions
Pre-AP: Strategies in Mathematics -- Chance, Variation, and Probability
As children learn to construct an understanding of the world around them, they base much of their knowledge on the predictability of the events that affect their lives. As they get older, this evolves into the study of the sciences and the behavior of our world. Quantifying unpredictable events proves to be difficult for students at many levels, but this skill is important in the study of real-life phenomena. Teaching the concept of chance is daunting; research shows that humans fail to reason optimally about chance, even after taking courses in probability and statistics. Advances in technology, too, make the teaching of chance, variation, and probability very different than in the past, and many of today's instructors find this their least comfortable discipline.
This one-day workshop uses recent research on the learning of probability to engage teachers in classroom activities that enable students to analyze and understand chance events. The activities progress through elementary definitions and concepts of probability, culminating in the use of simulation to model probability problems. Participants gain significant knowledge about finding and correcting student misinterpretations about these events, and they discover ways to improve student understanding through reflection and communication. Teachers learn to develop activities for the classroom that help connect the content to events relevant to students and their lives. Specific topics include classical probability, law of large numbers, and probability rules, distributions, and conditions.
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Pre-AP: Strategies in Mathematics -- Chance, Variation, and Probability
Pre-AP: Strategies in Mathematics -- Helping Students Learn Mathematics Through Problem Solving
Students who engage in active questioning, analysis, construction, and communication have been shown to have deeper understanding of the concepts they learn, in contrast to the traditional teaching model of memorization and repetition. Since most of today's mathematics teachers were taught traditionally, they often feel a weakness in developing learning through activities and problems. Most teachers have gone to great lengths in evolving their classrooms, but still may not feel comfortable or effective.
This two-day workshop provides strategies for designing and using meaningful investigations, writing dynamic problems, and enhancing current classroom activities so that students will develop deeper understanding and produce more thoughtful responses. Teachers will gain an understanding of how successful students learn and how to develop those skills in others, as well as how to build relevant, informative assessments that allow teachers to monitor and foster mathematical thinking without interrupting instruction.
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Pre-AP: Strategies in Mathematics -- Helping Students Learn Mathematics Through Problem Solving
Pre-AP: Advanced Topics for AP Vertical Teams in Mathematics -- Assessment
This one-day workshop teaches middle and high school math teachers techniques of assessment designed to support instruction for students as active learners and problem solvers. Educators increasingly recognize that the purpose of classroom assessment of student achievement is to help teachers make decisions about instruction. Assessments, reliability, validity, scoring guidelines, and performance appraisals are the key topics covered in this workshop.
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Pre-AP: Advanced Topics for AP Vertical Teams® in Mathematics--Assessments
Pre-AP: Developing Algebraic Thinking
This one-day workshop is for mathematics teachers in grades 6 to 10. It provides teachers with hands-on activities and techniques to help students develop algebraic reasoning. A key feature of this workshop is the use of graphing calculators to help students visualize and explore algebra from graphic, numerical, and analytical perspectives as well as from traditional symbolic representations. Objectives for participants in this workshop include learning to develop techniques by using inquiry learning in teaching algebraic thinking, using patterns to find relationships, using tables in investigating relationships, and describing patterns using both recursive and closed relationships.
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Pre-AP: Strategies in Mathematics - Developing Algebraic Thinking
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