How We Teach
How is Math Taught at Mt. Hood Community College?
In an effort to orient new faculty to the culture of the Mt. Hood Math Department, we have tried to summarize our department norms, our classroom environment and our perspective as instructors. We hope this document might also be informative for other professionals and perhaps for students as well.
Communication is important not only for our students but also for us. Our consistency, our curriculum, our identity as a department depends on dialogue – dialogue within our department, with areas that we serve inside the college, with others in our profession.
Consistency in Department
We make decisions as a whole department, through discussion, and consensus. These decisions include all areas of our practice – pedagogy, curriculum, text selection, assessment, etc. Through continuing discussion, we maintain consistency from class to class, independent of instructor. However, there remains room for individual interpretation and application within those agreements. It is especially important that all instructors engage in regular peer-to-peer dialogue to maintain consistency while allowing for individual style. Weekly meetings with level teams are one of the more effective methods for this collaboration.
Our curriculum is designed through dialogue. We do not simply select a text and follow the table of contents. Rather, we have designed the entire math sequence based on a few questions:
- What do students need to know about mathematics? At what level?
- When do students need to know a particular math concept/skill? We want to teach skills when they are needed and can be applied, and in preparation for the next class. For example, we want to teach skills needed only for calculus in a calculus or precalculus class, but not in beginning algebra.
- Why do students need to know a particular math concept/skill? Is the knowledge needed for application, to prepare for an upcoming math class, for life in general?
- What are the recommendations from the AMATYC and NCTM Standards?
Through this process, we have created course outlines that define what will be taught in a course. It is nearly impossible to find a textbook that covers all the material with the emphasis we need (conceptual, application, exploration). Thus, some instructors have chosen to write textbooks at some levels. At other levels, instructors must still supplement available texts as needed to cover the curriculum. This commitment to teaching the curriculum, rather than a textbook, drives Mt. Hood mathematics instruction.
An atmosphere of exploration is fundamental to the math program at Mt. Hood. Students learn by asking questions of the instructor, of each other, of the calculator. Students learn to form their own questions about mathematics; “What if we changed . . . ?”, “How does this relate to . . . ?” Students learn by building upon their knowledge and experiences, not because the instructor imposes his/her understanding of the material on the students and expects students to mimic his/her process. We try to encourage a desire to know “why” and a curiosity about “what if,” rather than just teaching “how.”
Research shows that students better understand, retain, and transfer knowledge gained when they are active in the learning process. Options for involving students include: exploration, group work, application problems, problem solving experiences, prepared & guided activities, question & answer format, and technology-based activities. A lecture environment can be interactive but often involves only a few students and does not substitute for other activities that involve all students.
The team-learning environment at Mt. Hood may be different from other group experiences. While nearly all evaluation is performed individually, teams are used for problem solving, to develop ideas, to communicate, to explore, and to discover mathematics. Teams also foster a positive classroom environment by providing students with opportunities to help each other, to learn by teaching, and to see a variety of approaches. Research shows that an individual understands more if s/he can explain their understanding to another person. Meeting this goal requires peer interaction.
In a learning environment, the team works on the same task, brainstorming, sharing ideas, problem solving, learning new ways to think, learning by listening, learning by talking. The desired outcome is for each student to gain knowledge of the topic, independent of the group.
In contrast, a team in a work environment may split up the necessary tasks and put their work together to create a final product. This final product is the outcome. At times, we may allow students to work together on a team product for evaluation. We suggest a working model that still emphasizes the outcome of personal knowledge.
Techniques, concepts, and applications are integrated. The applications motivate the need for theory and techniques. The conceptual understanding helps students recognize when a particular math skill could be applied. Teaching the applications simultaneously satisfies the students’ thirst to know why they are learning math.
Students should understand the mathematical concepts, not just the procedures. Active discovery learning, class discussions, team problem solving, and communication expectations facilitate this conceptual understanding. The instructor should regularly use conceptual explanations in answering questions and in presenting information.
Communication is an important ability in any field. We teach the careful, accurate use of vocabulary and notation to support clear, precise communication of mathematical ideas and processes. Students practice verbal communication skills in group and whole-class discussions. Reading skills are made necessary by the nature of the materials used. Evaluation is designed to use the math vocabulary and to require the appropriate reading level. Written communication is demonstrated through evaluation of problem solving and applications write-ups. Translating math into reading, writing, and verbal communication helps in conceptual understanding.
To support the importance of applications, concepts, and communication, a grading scheme should assess all of these in addition to skills.
We implement technology at all levels of math as an explorative tool as well as a computational tool.
Diversity of Student Population
Our students are diverse in learning styles, math background, career goals, school goals (transfer vs. technical vs. personal enrichment), as well as the usual measures of diversity. These variations enhance the classroom environment by providing a variety of strengths that all can build upon.
Educational research shows that students who make connections with others at their college have higher retention and persistence rates. The team environment of the math classroom at Mt. Hood encourages students to build community. In addition, teams allow students to problem solve from many different viewpoints, to build on diverse strengths (skills, application experience, conceptual understanding), to reduce math anxiety through shared experience. In a team, every student has a chance to be the expert and to be the learner.
Students may arrive with barriers to success in our classes. As instructors, we try to help students recognize these barriers and suggest strategies/resources for improving their likelihood of success. Throughout the term, the college offers student success workshops on dealing with issues such as math anxiety, testing problems, study skills and organizational skills. Many instructors give suggestions for dealing with family/job demands, inadequate study time, etc. The Learning Assistance Center offers tutoring and testing services.
To support student success, we enforce the reading and writing prerequisites for our math courses.
Prerequisites help individuals succeed and make the class a more equitable group, necessary for a successful team-learning environment.
Instructor Preparation & Knowledge
As a result of our classroom environment, students may ask questions that are new to the instructor. The instructor must have an adequate depth of mathematical knowledge to answer these questions clearly. On rare occasions the instructor must be willing to answer “I don’t know, I will get back to you,” and have the resources and time to follow through.
Sharing vs. Individual Responsibility
Our department works collaboratively. Instructors share class plans, assignments, tests, activities, etc. It is especially important that instructors teaching any course for the first time learn the curriculum, pedagogy, and assessment techniques from others’ examples, and that every instructor be prepared to share materials. Before using newly designed exams or activities, it is preferred to invite comments from other instructors about clarity, timing, content, and level. Testing activities prior to class helps avoid student frustration and ineffective use of class time.
Feel free to consult with other faculty to obtain feedback on your evaluation activities and materials. The math faculty is very willing to make suggestions about materials before you use them in your course.
There are many resources available to expand on the ideas and expectations expressed here. Your colleagues are always happy to confer, share, and problem solve together. If you prefer to start with written documentation, there is a notebook with a compilation of suggestions available in the department office, located with the textbooks. Please borrow the notebook and read or copy what you need, when you need it. We are excited about sharing the work of educating our students. Welcome!