MATHEMATICS PROGRAM MODELS FOR OHIO HIGH SCHOOLS
The ODE Mathematics
Program Models offer six (6) different sequences of courses that take an applications,
blended, or connected approach to the high school mathematics curriculum. The ORC
Pacing Guides (upper left navigation bar) feature a schedule of topics, links to
best practice lessons, teaching tips, and rich problems to engage students in exploration,
analysis, and application of big ideas in mathematics.
(Below is a brief summary of Ohio Department of Education draft, June 2006)
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In Ohio, the commitment is that all students will graduate from high school fully prepared for the demands of the workplace and further study. There are many ways a curriculum can be configured to respond to this commitment. In the area of secondary mathematics, the Department of Education has developed three different models for mathematics programs in grades 9-12.
The mathematics content for the Models is specified in five of the Ohio Academic Content Standards: Number, Number Sense and Operations; Measurement; Geometry and Spatial Sense; Patterns, Functions and Algebra; Data Analysis and Probability. Equally important for effective curricula and for student learning is the sixth standard, Mathematical Processes, which includes five strands: problem solving, reasoning, communication, representation, and connections.
Authentic problem solving requires students not simply to get an answer but to develop
strategies to analyze and investigate problem contexts.
Reasoning involves examining patterns,
making and testing conjectures, and creating and evaluating arguments. Oral and written
skills give students tools for sharing ideas and clarifying their understanding
of mathematical ideas. Mathematics uses many different forms of numerical, algebraic, geometric,
and physical representation to embody mathematical concepts and relationships. A coherent
curriculum will help students make connections
between mathematical concepts and between mathematics
and other subjects they study. In the Program Models, these mathematical processes are developed
through course design and through experiences with rich contextual problems.
Descriptions of the Mathematics Program Models
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The models are presented in terms of years of study (Year 1 through Year 5), recognizing that some students will start the secondary mathematics curriculum in grade 8 and others in grade 9. The models emphasize the importance of every student taking mathematics in each of the four years of high school, and they provide appropriate courses for all students in grade 12.
Characteristics Common to All Three Program Models
Although the models offer distinctive ways of approaching the mathematics described in the Ohio Academic Content Standards, they share several basic characteristics.
- Each demonstrates how the Standards can be implemented through a curriculum and how instruction can be organized to improve student learning;
- Each prepares students to achieve or exceed the proficiency level on the mathematics portion of the Ohio Graduation Test in grade 10 and to achieve or exceed the requirements to enter Ohio college and university mathematics courses above the remedial level by the end of the Year 3 course;
- Each clarifies where the emphases need to be in instruction and what the foci are for each course;
- Each moves students from informal experiences and intuitive understanding to levels of formal definition and logical reasoning;
- Each displays the connectedness and coherence of the mathematics studied in each course and across the courses in a sequence.
- Each assumes appropriate use of technology with dual goals: (1) student proficiency with foundational skills and basic mathematical concepts using basic manual algorithms and (2) student competency in using appropriate technology to encourage mathematical exploration and enhance understanding.
Distinctive Characteristics of the Three Models
This model uses the applications
of mathematics to motivate mathematical topics in algebra and geometry.
Model B This model blends
the mathematics of the various content strands. Data topics are woven throughout the model with a data project in Year 3.
Model C. This model features a
classic sequence of courses that emphasizes connections
across content strands. Data analysis topics have been added to the familiar high school mathematics curriculum.
Each of Models A, B, and C prepares students to take a calculus course in their first year of college. Model A',
Model B', and Model C', provide curricula for students who
will probably not study calculus.
Possible Course Sequences