Summer Workshop Plans

Summer Workshop Agenda

In the summer of 1998, RMTC organized and conducted six one-week workshops, one for Course 1, three for Course 2 and two for Course 3. The broad goals of the Course 1 - 3 workshops were:

• to assist teachers in gaining an understanding of the mathematical content in CPMP;

• to model instructional and assessment practices for effective implementation of CPMP;

• to address issues of concern raised by participants, such as classroom management and student achievement;

• to assist participants in understanding the scope and sequence of the three-year curriculum in the context of the development of mathematical concepts in each course level.

To read more about the RMTC project Summer Sessions, visit their project website.

Course 1 Agenda

Monday
8:00	Refreshments
8:30	Introductions Why reform mathematics programs? Pretest on Course 1 content
10:30	Overview of the Statistics and Probability Strand Facilitating collaborative groups Modeling of instruction of Unit 1, Patterns in Data Content objectives for Unit 1: To use various graphical displays of data to uncover important patterns in the data set and interpret these patterns for a real-world context To summarize and interpret sets of data using measures of center and variability To compare sets of data using scatterplots and the line y = x, and to interpret these comparisons for the real-world contexts that gave rise to the data
4:45	Synthesis of the day's work Dismissal
Tuesday
8:00	Continued work on Patterns in Data
1:00	Overview of the Algebra and Functions Strand Modeling instruction of Unit 2, Patterns in Change Content objectives for Unit 2 To begin developing students' sensitivity to the rich variety of situations in which quantities vary in relation to each other To develop students' ability to represent relations among variables in several ways - using tables of numerical data, coordinate graphs, symbolic rules, and verbal descriptions - and to interpret data presented in any one of those forms To develop students' ability to recognize important patterns of change in single variables and related variables
4:45	Synthesis of the day's work Dismissal
Wednesday
8:00	Continued work on Patterns in Change
10:30	Modeling instruction of Unit 3, Linear Models Content objectives for Unit 3 To begin developing students' sensitivity to the rich variety of situations in which quantities vary in relation to each other To develop students' ability to represent relations among variables in several ways - using tables of numerical data, coordinate graphs, symbolic rules, and verbal descriptions - and to interpret data presented in any one of those forms To develop students' ability to recognize important patterns of change in single variables and related variables
4:45	Synthesis of the day's work Dismissal
Thursday
8:00	Overview of the Discrete Mathematics Strand Modeling instruction of Unit 4, Graph Models Content objectives for Unit 4 To use vertex-edge graphs to make sense of situations involving relationships among a finite number of elements - for example, conflict and prerequisite relationships To gain experience in mathematical modeling by building and using vertex-edge graph models to solve problems in a variety of real-world settings To develop the skill of algorithmic problem solving: designing, using, and analyzing systematic procedures for solving problems To investigate and apply three powerful and widely used graph models: Euler paths, vertex coloring, and critical paths
1:00	Overview of the Geometry and Trigonometry Strand Modeling instruction of Unit 5, Patterns in Space and Visualization Content objectives for Unit 5 To use geometric shapes and their properties to make sense of situations involving data, change, chance, and discrete structures To use visualization to interpret and reason about space and plane situations To classify, construct, and sketch models of space-shapes To use plane- and space-shapes to model real-life situations To find appropriate measures (perimeter, area, volume) of plane-and space-shapes To classify polygons and analyze their properties To identify and explain different kinds of symmetry for plane-and space-shapes
4:45	Synthesis of the day's work Dismissal
Friday
8:00	Continued work on Patterns in Space and Visualization
3:00	Synthesis of the day's work Posttest Workshop Evaluation Dismissal

Course 2, Agenda

Monday
8:00	Refreshments
8:30	Introductions Pretest on Course 2 content
9:30	Modeling of instruction of Unit 1, Matrix Models Content objectives for Unit 1: To see the interconnectedness of mathematics through the use of matrices to explore topics in algebra, geometry, statistics, probability, and discrete mathematics To use matrices for organizing and displaying data in a variety of real-world settings like brand switching, tracking pollution through an ecosystem, and tournament rankings To develop further the skill of mathematical modeling by building matrix models and then operating on them to solve problems To learn and apply matrix operations: row sums, scalar multiplication, addition, subtraction, and matrix multiplication To use matrices and inverse matrices to answer questions that involve systems of linear equations
4:45	Synthesis of the day's work Dismissal
Tuesday
8:00	Modeling instruction of Unit 2, Patterns in Location, Shape, and Size Content objectives for Unit 2 To use coordinates to model points, lines, and geometric shapes in the plane and to analyze the properties of lines and shapes To write systems of linear equations that model real-life situations, to solve systems using linear combinations, and to explain the geometry behind this method To use coordinate geometry and programming techniques as a tool to implement computational algorithms, model transformations, and investigate the properties of shapes that are preserved under transformations To build and use matrix representations to model polygons, transformations, and computer animations
1:00	Programming Animation on graphics calculators
4:45	Synthesis of the day's work Dismissal
Wednesday
8:00	Modeling instruction of Unit 3, Patterns of Association Content objectives for Unit 3 To describe the association between two variables by interpreting a scatterplot To interpret correlation coefficients To understand that just because two variables are correlated, it does not mean that one directly causes the other To know when it is appropriate to make predictions from the least squares regression line or its equation To understand the effects of outliers on correlation coefficients, on the equation of the least squares regression line, and on the interpretations of correlation coefficients and regression line in real-world
1:00	Modeling instruction of Unit 4, Power Models Content objectives for Unit 4
4:45	Synthesis of the day's work Dismissal
Thursday
8:00	Continued work on Unit 4 - Quadratic Models
10:15	Modeling instruction of Unit 5, Network Optimization Content objectives for Unit 5 To gain experience in mathematical modeling by building and using vertex-edge graph models to solve problems in a variety of real-world settings To develop the skill of algorithmic problem solving by designing, using, and analyzing systematic procedures for solving problems To optimize networks in different ways and in different contexts by finding minimal spanning trees, shortest paths, Hamiltonian paths, and by analyzing the Traveling Salesperson Problem
4:45	Synthesis of the day's work Dismissal
Friday
8:00	Unit 8, Capstone - Investigations 2 - 7 To review the major objectives of the course in the context of one large project To synthesize mathematical concepts from Course 2
11:00	Posttest Workshop Evaluation
1:00	Capstone Group Presentations
4:00	Dismissal

Course 3, Agenda

Monday
8:00	Refreshments
8:30	Introductions
10:30	Overview of the algebra strand in Course 3 Modeling of instruction of Unit 1, Multiple Variable Models Content objectives for Unit 1: To develop an understanding of, and the ability to solve, problems involving multiple-variable relations (including trigonometric relations) where one equation relates more than two variables To develop the ability to solve multiple-variable equations for one variable in terms of the other variables To model situations with systems of equations and inequalities where two or more output variables are related to the same input variables, and to apply those systems to solve problems
3:15	Modeling of instruction of Unit 3, Symbol Sense and Algebraic Reasoning
4:45	Synthesis of the day's work Dismissal
Tuesday
8:00	Continued work on Symbol Sense and Algebraic Reasoning Content objectives for Unit 6
10:15	Modeling instruction of Unit 6, Families of Functions Content objectives for Unit 6 To describe the table and graph patterns expected in linear, direct power, inverse power, exponential, sine, cosine, absolute value, and square root models given the corresponding algebraic rules in function form To identify a function as a variation of a basic family of functions To recognize how the patterns in graphs, tables, and rules of functions relate to the functions' transformed graphs, tables, and rules To write function rules which are reflections across the x-axis, translations, or stretches (or combinations of these transformations) of basic functions To apply all of the transformation above as they relate to real-world situations
4:45	Synthesis of the day's work Dismissal
Wednesday
8:00	Modeling instruction of Unit 2, Modeling Public Opinion Content objectives for Unit 2 To measure and analyze public opinion through a mathematical analysis of voting and surveys To use and analyze a variety of election analysis methods, particularly those based on preferential voting To understand and apply basic ideas related to the design and interpretation of surveys, such as background information, random sampling, and bias To construct simulated sampling distributions of sample proportions, and to use sampling distributions to identify which proportions are likely to be found in a sample of a given size To construct and interpret margin of error and confidence intervals for population proportions To critically analyze surveys and elections in everyday life and as reported in the media
2:15	Modeling instruction of Unit 4, Shapes and Geometric Reasoning Content objectives for Unit 4 To recognize the differences between, as well as the complementary nature of, inductive and deductive reasoning To develop some facility in producing deductive arguments in geometric situations To know and be able to use the relations among the angles formed when two lines intersect To know and be able to use the necessary and sufficient conditions for two lines to be parallel To know and be able to use triangle similarity and congruence theorems To know and be able to use the necessary and sufficient conditions for quadrilaterals to be (special) parallelograms To use a variety of conditions among triangles, lines, and quadrilaterals to prove the correctness of related geometric statements or provide counterexamples
4:45	Synthesis of the day's work Dismissal
Thursday
8:00	Continued work on Shapes and Geometric Reasoning
1:00	Modeling instruction of Unit 5, Patterns in Variation Content objectives for Unit 5 To understand the standard deviation as a measure of variability in a distribution To understand the normal distribution as a model of variability To understand and be able to use the number of standard deviations from the mean as a measure of position of a value in a distribution To understand the construction, interpretation, and theory of control charts To understand and apply the Addition Rule for mutually exclusive events
4:45	Synthesis of the day's work Dismissal
Friday
8:00	Continued work on Patterns in Variation
10:15	Modeling instruction of Unit 7, Discrete Models of Change Content objectives for Unit 5 To use iteration and recursion as tools to represent, analyze, and solve problems involving sequential change To formalize and consolidate previous study of NOW-NEXT equations, particularly through the use of subscript notation and the introduction of recursion equations To understand and apply arithmetic and geometric sequences, and series To understand and apply the method of finite differences To explore function iteration and, in the process, informally introduce function composition To investigate and apply recursion equations, particularly combined recursion equations of the form An = r An - 1 + b To review linear, exponential, and polynomial models from a recursive perspective
4:00	Synthesis of the day's work Workshop Evaluation Dismissal