Home » Programs of Study » Mathematics » General Instructional Methods

General Instructional Methods

The MHCC Mathematics Curriculum emphasizes conceptual understanding, real-world applications, multiple representations of problem situations, making connections, mathematical modeling and mathematical problem solving. This represents a shift away from technique mastery and procedural skills. For students to see mathematics as an integrated whole, course objectives should be presented in a connected fashion and not treated as discrete topics or concepts.

Calculator: The calculator is required for the course to support a focus on conceptual understanding and applications rather than emphasizing algorithms. A student's grade should not depend on their knowledge of arithmetic algorithms. The calculator should be used as a tool to clarify material and speed computation, not as a substitute for explaining the reasons behind the mathematics. Estimating skills (without the calculator) and reality checks should be emphasized to verify calculator results. In addition, technology is a component of the real world for which we are preparing our students. We must encourage tehnological as well as mathematical literacy.

Language: Use the language of mathematics as you teach. For example, refer to the denominator of a fraction as the denominator more and more frequently through the term (rather than as the "bottom").

Learning Environment: Students learn in many different ways: by writing, by listening, by discussing, by asking, by explaining, by reading, etc. The classroom should be structured to support these many learning styles. Thus, teaching should involve a variety of presentations including such methods as:

In addition, out of class work should also include a variety of learning approaches including:

The classroom should be a cooperative environment managed by the instructor, but focused on the students. Thus, neither a complete lecture format nor a team-based classroom left alone is a successful model. Balance of learning environments and instructor supervision and contribution are necessary components. Although the balance of activities in a classroom varies between instructors, a successful learning environment will certainly include the following essential components:

• Problem solving activities must be provided for the students to develop and apply a variety of strategies to solve problems, verify and interpret results with respect to the original problem situation, and generalize solutions and strategies to new problem situations. Through this experience students acquire confidence in using mathematics meaningfully and are able to formulate and solve problems as they exist in the real world and in their field or area of interest.

• Concepts presented in a class should lead to applications in areas such as natural resources, human resources, health services, business and management, industrial and engineering technology, and arts and communication. Through contextual learning, students are able to value the role of mathematics in our culture and ever-changing technological society.

• Guided discovery learning activities must be provided to help the student take responsibility for his/her learning and develop a mechanism to "learn how to learn." By investigating patterns and exploring concrete, pictorial, and graphical models, students create their own understanding of mathematical concepts. Discovery activities also teach students to be adventuresome in their approach to problems - that they need not know the answer before beginning to try something. Manipulatives must be available to aid guided discovery learning activities.

• Teams should be constructed to best allow for whole team discussion without any students being left out. Teams should work together in class most days on tasks furthering their understanding of the material and their problem solving/communication abilities. Most discovery activities are completed in teams. (It is recommended that your teams be comprised of no more than five students due to the tables used in our classrooms.)

• Although teams are an extremely important and valuable learning environment, they cannot replace whole class discussions where students share their insights in an interactive lecture with the instructor as the knowledgeable authority. Team activities (especially discovery activities) need to be followed by a discussion/lecture to ensure that all students understand the material.

• To help coordinate these follow-up efforts and to ensure that your class is learning the material, you should be constantly assessing their progress while students are working in teams. Teamwork is not a break for the instructor. You need to be available to answer questions, sometimes guide discussions, facilitate good team behaviors as needed, and gather information about your students' comprehension and ideas.
  This type of assessment will help you select and set up your next learning environment wisely (or adjust the current one as necessary). As students are working on an activity, you may realize that some instructor-led discussion is necessary in the middle rather than just at the end (as you might have planned). You can use your observations to decide whether you should follow a team problem solving session with a class discussion, a lecture, or by having each team put their solution on the board and giving the teams an opportunity to present their approaches. Flexibility is an extremely important part of teaching in a student-centered learning environment.
  Although flexibility is important, you must remember that the course outline must be covered by the end of the term. Sometimes you may need to leave a topic that students are not comfortable with and continue covering material. It is important to spiral back and address these weaker points as the term continues.

Specific Evaluation Criteria For Student Learning
And Minimum Acceptable Level Of Performance

Passing this course with a C or better serves as a prerequisite for other courses. This requires attention to the amount of verifiable individual work completed by the student. You must give a cumulative in-class final exam to help ensure that students are truly prepared for the next course.

Grades should be based on a balanced variety of grading opportunities spread throughout the term. Although you may not choose to use every method below, a variety of methods is expected. Student evaluation must include problems or activities that incorporate and integrate several outcomes, and closely resemble situations that exist in the real world.