Registration Information



Registration Information

Professional Development for Transition to College Mathematics

Fee: The registration fee is payable in advance by check or purchase order. The fee includes the four-day workshop, follow-up session(s), continental breakfast, lunch, and all workshop materials. Other meals, lodging, and travel are not included.

Confirmation: Within two weeks of receiving your registration form, we will mail or FAX your confirmation. Priority will be give to teams of teachers from schools that will implement at least one class of Transition to College Mathematics during the 1999-2000 school year.

Cancellation and Substitutions: Cancellations may be made up to two weeks prior to the workshop. No-shows or cancellations after 14 days prior to the workshop are payable and are not refundable. Substitutions may be made at any time at no additional cost.

Hotel Accommodations: Please make your own hotel reservations directly with the hotel at least three weeks in advance. To assure that you receive the workshop rate, be sure to mention the Algebra Institute to the hotel when making your reservation.

Certificate of Completion: We will provide on site, verification that you have completed 24 contact hours of continuing education. Teachers should apply to their own district for local or state credit.

Attire: We recommend that you wear casual and comfortable clothing and bring a sweater or jacket in case the room is cool.

The goal of the three summer institutes is to address the objectives of the fourth year course, Transition to College Math. The course description is included in this memo.

Algebra Seminar: Transition to College Math

Fifteen pilot schools (30 teachers) will be selected.

Dates: July 6-9, 1999 Location: Little Rock Hilton

The institute will enable teachers to use applications and the TI-83 graphing calculator in the teaching of algebra and statistics topics by providing hands-on experiences and by modeling effective strategies for teaching. Each participant will receive a packet of institute materials including a copy of Advanced Algebra Through Data Exploration: A Graphing Calculator Approach textbook from Key Curriculum Press, a teacher’s guide and answer key, Calculator Notes, and other institute materials.

Integrated Algebra Seminar: Transition to College Math

Fifteen pilot schools (30 teachers) will be selected.

Dates: July 27-30, 1999 Location: Little Rock Hilton

The institute will enable teachers to use applications and the TI-83 graphing calculator to address the objectives of the Transition Math syllabus. Each participant will receive a custom designed text that includes the following units from the SIMMS integrated mathematics program: Yesterday’s Food, If the Shoe Fits, Skeeters, AIDS, Rock Bands, Atomic Clocks, Banking, Graphing the Distance, Marvelous Matrices, Who Gets What and Why?, Game of Life, And the Survey Says, Confidence Builder, and To Null or Not to Null. Teacher notes and solution keys will also be included in the institute materials.

Pacesetter Mathematics: The College Board

Ten pilot schools (20 teachers) will be selected.

Call The College Board Pacesetter representative, Debbie Kusek, at 1-800-416-5137 for sample materials, program description, and complete College Board registration information.

REGISTRATION FORM

Transition to College Mathematics Professional Development Institute

Please check the professional development seminar for which you are applying. Early enrollment is recommended. Each seminar is limited to 30 participants.

____ Algebra Seminar: Key Curriculum Press Dates: July 6-9, 1999

Location: Little Rock Hilton Phone: 501-664-5020

Registration fee per teacher: $100.00 Make check or P.O. payable to ASSI.

Note: Priority will be given to teachers in schools that pilot the Transition course in 1999-2000.

Those teachers will receive a $50 per day stipend for the summer training.

____ Integrated Algebra Seminar: SIMMS Professional Development Dates: July 27-30, 1999

Location: Little Rock Hilton Phone: 501-664-5020

Registration fee per teacher: $100.00 Make check or P.O. payable to ASSI

Note: Priority will be given to teachers in schools that pilot the Transition course in 1999-2000.

Those teachers will receive a $50 per day stipend for the summer training.

____ Pacesetter Mathematics: The College Board Dates: July 13-16, 1999

Follow-up dates: October 21-23, 1999; two days - spring, 2000

Location: Riverfront Hilton, North Little Rock Phone: 501-371-9818

Registration fee per teacher: $1350.00 A check or P.O. will be payable to the College Board upon completion of additional registration information required by The College Board.Note: Priority will be given to teacher in schools that implement the Pacesetter course in 1999-2000. School districts of those teachers will be reimbursed $600.00 of the registration fee upon completion of the summer institute.

Name:_________________________________________ Home Phone (____)_______________

Home Address:_________________________________________________________________

City:______________________________________ State: AR Zip:______________________

School District:_________________________________ County:_________________________

School Name:___________________________________ School Phone (____)______________

School Address__________________________________ School Fax (____)________________

City:______________________________________ State: AR Zip:______________________

Mail completed registration to Arkansas Department of Higher Education, ATTN: Judy Trowell, 114 East Capitol Avenue, Little Rock, Arkansas 72201 or fax to (501) 371-2008. For additional information, call Judy Trowell or Suzanne Mitchell at (501) 371-2060 or Roy Barnes at (501) 682-5296.

MATHEMATICS

College Entry Level Expectations

The entering college student must master certain mathematical concepts in high school mathematics courses in order to be successful in an entry level college mathematics course Χ College Algebra or its equivalent. Mathematics preparation should include a sound foundation in the following:

1. Numerical operations 7. Elementary statistics and probability

2. Algebraic skills 8. Problem solving

3. Geometric concepts 9. Representation

4. Measurement 10. Communication

5. Estimation 11. Technology

6. Number sense 12. Mathematical modeling/functions

Students in College Algebra or other college mathematics courses must be prepared to represent, manipulate, and validate mathematical concepts. Thus, mathematical preparation in high school should provide students with competencies that include the ability to develop, test, and explain assumptions about number, algebra, geometry, and probability and statistics using formal and informal reasoning.

The following strands underlie a sound mathematical foundation and support mastery of quantitative competencies and mathematical skills:

Strand 1: Problem Solving

Students will develop the flexibility, perseverance, and creativity that are characteristic of good problem solvers even when no routine path is apparent.

Strand 2: Communication

Students will be able to communicate the reasoning used in solving problems both orally and in writing.

Strand 3: Representation

Students will effectively use a variety of representations as reasoning tools.

Strand 4: Technology

Students will know how to choose and use appropriate technology and recognize the usefulness and limitations of technology.

Guidelines for College-entry Mathematics Preparation

A common experience of faculty who interact with students in college and university freshmen mathematics courses is to confront the following student comment: “I don’t understand what they want in this problem. Just tell me what to do and I’ll do it.” The areas of mathematics and skills listed below are interrelated and are not intended to emphasize mathematics as a list of discrete topics. However, they are intended to provide guidelines for mathematical experiences that will prepare students for success in college entry-level mathematics.

A student entering College Algebra (or its equivalent) is expected to understand and apply:

1. the operations and vocabulary of numerical concepts and computation;

2. algebraic concepts related to patterns, relations, and functions;

3. linear and spatial relationships and other concepts of geometry;

4. introductory concepts of probability and statistics.

Mathematical competencies should be demonstrated through the successful performance of the following:

I. Number Systems Concepts: Students entering college should understand and use numerical concepts and computation, demonstrate number sense, and apply proportional reasoning. They will be expected to:

5. Know the vocabulary for computation and be able to describe number groups and operations (i.e., even, prime, exponents, absolute value, scientific notation, etc.).

6. Perform basic arithmetic operations involving whole numbers, integers, decimals, fractions, real and complex numbers (i.e., addition, subtraction, multiplication, division).

7. Select and use appropriate arithmetic operation for solving multi-step problems.

8. Estimate solutions and determine reasonableness of answers.

9. Demonstrate number sense using whole numbers, fractions, decimals, integers, irrational and complex numbers.

10. Apply ratios, proportion, and percent in a variety of situations.

11. Solve problems using appropriate calculation methods (i.e., mental arithmetic, estimation, paper and pencil, calculator, or computer.).

12. Know number relations such as divisors, multiples, greatest common divisor, least common multiple, primes, etc.

II. Algebraic Concepts: Students entering college should demonstrate competency in the use of variables, functions, and graphs to model applications. They will be expected to use algebraic operations and manipulations to solve a variety of equations and inequalities, including the ability to:

13. Recognize and use multiple representations of functions.

14. Solve equations and inequalities using a variety of techniques, and verify solutions.

15. Understand the concept of function.

16. Use the domain and range functions in a variety of ways.

17. Create models of “real” world situations using absolute value, polynomial, and exponential functions.

18. Represent and use rates of change.

19. Graph and interpret family of functions and relations.

20. Recognize and understand the concepts of arithmetic and geometric sequences.

21. Use matrix algebra.

III. Geometric Concepts: Students entering college should understand relationships in geometric figures (both two- and three-dimensional) and utilize these relationships to create geometric models. They will be expected to:

22. Understand and use vocabulary (i.e., congruency, similarity, symmetry, transformations).

23. Use appropriate units of measurement and convert units in problem solving situations.

24. Select and apply formulas to calculate perimeter, area and volume of geometric shapes.

25. Describe geometric relations algebraically (i.e., coordinate geometry).

26. Graph equations and relationships to grasp the principles that

- a graph represents all the values that satisfy an equation, and

- the values that satisfy two equations are found where their graphs intersect.

27. Sketch and interpret two- and three-dimensional figures.

28. Apply trigonometric ratios to problem solving (i.e., using formulas or scale drawings to calculate distances and angles that are inconvenient to measure directly).

29. Develop and analyze conjectures from geometric models.

30. Use similarities in proportional reasoning.

IV. Probability and Statistics Concepts: Students entering college should understand and use the introductory concepts of probability and statistics. They will be expected to:

31. Compute and interpret the mean, mode, median, range, and standard deviation for a given data set.

32. Represent and interpret data pictorially (i.e., histogram, bar chart, etc.).

33. Formulate a decision based on an analysis of data.

34. Collect empirical data and generate random data.

35. Assign correct probabilities to simple random events.

36. Use counting techniques to determine probability (i.e., combinations and permutations).

37. Select appropriate technology to aid in data analysis and representation.

38. Recognize inappropriate use of data.

College Prep Math: Transition to College Mathematics

College Prep Math: Transition to College Mathematics is intended to build on previous courses in Algebra I, Geometry, and Algebra II (or their equivalents in multi-year integrated programs) and to place emphasis on bringing about a deeper understanding of those mathematical relationships. This course may be completed to satisfy the fourth year of mathematics required for unconditional admission to Arkansas’ colleges and universities.

The course syllabus is divided into four modules and is presented as a flexible plan that includes topic structure and content emphasis, but does not specify a given textbook or fully prescribed curriculum. The topics are designed to fit with current textbook materials and to articulate the competencies required for entry level postsecondary mathematics courses.

It is recommended that emphasis throughout the course be placed on numerical and graphical representations, modeling from data, reasoning clearly and communicating concepts via writing, speaking, listening, drawing, and reading, and integrating technology as a tool for developing a deeper understanding of mathematical structure. The statistics strand is incorporated throughout as students create models for a set of data, write an equation for the model, and use it to make predictions or estimates. Ongoing emphasis should be placed on helping students develop study skills and time management that are critical for success in college. The curriculum delivery focus is on student learning. The context in which the mathematical content is developed should be carefully chosen to appeal to students without diminishing the importance and depth of the mathematics.

In addition to lesson quizzes and unit exams, student assessment should include alternative forms of assessment such as oral and written presentations, constructed response items with scoring rubrics, extended projects, and/or student journals and portfolios.

I. Constant Rate of Change: Linear Functions

? Simple Interest

? Constant Velocity

? Conversions

? Finding Cost

? Depreciation

? Recursive Modeling - Linear

The unit will build on students knowledge of linear equations and will use student-generated data to represent real-life situations in tables, graphs, and equations, emphasizing connections among these representations. For instance, they will be able to recognize a linear relationship represented by a table, by a graph, and by symbolic forms, particularly y = mx + b with b representing the initial condition and m representing the rate of change. Students will make predictions using recursion on the table, inspection on the graph, and algebraic manipulation on the model. Appropriate use of technology to use recursion and graphing will be essential in this unit.

2. Growth and Decay: Exponential Functions

? Compound Interest; Amortization; Annuities

? Population Growth and Decay

? Half-life; Radioactive Decay

? Chain letters; Pyramid Schemes

? Temperature Change

? Recursive Modeling - Geometric

The mathematics in this unit provides students with the opportunity to examine the nature of multiplicative change. Students will be able to recognize exponential growth or decay by creating tables, graphs and mathematical models. They will compare exponential models and make comparisons between linear and exponential models. Attention will be given to the limiting process that results in continuous growth (e). Technology must be used to model exponential growth and decay, produce accurate graphical representations, and develop an algebraic mathematical model through the regression process. Predictions may be made using recursion, inspection on the graph, and algebraic manipulation.

3. Describing the World: Mathematical Models

? Postal Rates

? Taxicab Geometry

? Mixture Problems

? Acceleration; Deceleration

? Sound

? Motion Graphs

? Communication Networks

? Matrices

Building on experiences with linear and exponential functions, students will broaden their ability to use mathematical models to describe a variety of situations. The unit will include continuous, noncontinuous, and discrete phenomena. Geometric and other algebraic models (i.e., quadratic, rational, etc.) will be used, with an emphasis on connections between tables and graphs and the symbolic form. Again, technology will be used to produce tables, graphs, and regression models. In this unit, the use of technology will be extended to produce simulations and geometric models.

4. Making Predictions and Describing Data: Probability and Statistics

? Life Expectancy

? Gaming Theory

? Sports

? Market Sampling

? Election Theory

In a data driven society, it is imperative that students learn to make decisions based upon appropriate analysis of data. This unit will provide a variety of opportunities for students to develop these skills. Mathematical topics of probability and descriptive statistics will form the basis for the content. Technology will be used to produce simulations, graphs, and to compute statistical measures of central tendency and variability.

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