The purpose of this page is to give faculty who are teaching a particular course for the first time an idea of how others treat the course. This page should be treated as a resource page, not as a dictate on how to teach a course.

One characteristic of our student population that makes teaching at a community college a wonderful and challenging profession is the diversity. I have had students as young as 8 and as old as 67 in my courses [said Bob Bradshaw]. Within the same class, there are exceptionaly bright students and others stuggling with concepts they learned long ago. It is our role to capture the interest of all the students in the course so that they all are able to make progress in meeting their goals.

## Course Listing

- MATH-101A Calculus I
- MATH-101B Calculus II
- MATH-101C Calculus III
- MATH-103 Linear Algebra
- MATH-104 Differential Equations
- MATH-111 Intro to MATLAB
- MATH-151 Algebra I
- MATH-151A/B Algebra I
- MATH-151A/B Self-paced Algebra I
- MATH-152 Algebra II
- MATH-152A/B Algebra II
- MATH-152A/B Self-paced Algebra II
- MATH-153 Intermediate Algebra
- MATH-153 Self-paced Intermediate Algebra

- MATH-155 Math for the Associate Degree
- MATH-156 Math for the Liberal Arts
- MATH-158
- MATH-159 Elements of Statistics and Probability
- MATH-167 Calculus for Business and Social Sciences
- MATH-181 Trigonometry
- MATH-188 Precalculus
- MATH-190 Basic Mathematics
- MATH-191 Prealgebra
- MATH-192 Basic Math and Prealgebra

To see how all the courses fit together, please refer to the Courses Flowchart.

## Math 101A Calculus I

### Teaching the Course

This course is designed for students majoring in math, engineering and the physical sciences. However, many students in the class will be majoring in business and the biological sciences. The emphasis should be placed on a thorough understanding of the concepts of calculus with a secondary emphasis on applications. In addition, since this may be the only course a student sees ε - δ proofs, the instructor should include coverage of the linear case.

### Technology

All students should be expected to have a graphing calculator and be encouraged to use it effectively. Instructors may want to take advantage of the availability of various software packages such as *Mathematica* and MATLAB for both demonstration purposes and student assignments. Students who transfer to four-year schools may need some experience with these packages. However, since the needs of the students will vary, mastery of the software should not be expected. Possible topics for software use are drawing tangent lines to a curve, comparing the graphs of a function and its first two derivatives, and estimating areas using Riemann sums.

## Math 101B Calculus II

### Teaching the Course

This course is designed for students majoring in math, engineering and the physical sciences. However, many students in the class will be majoring in business and the biological sciences. The emphasis should be placed on a thorough understanding of the concepts of calculus with a secondary emphasis on applications. Integration plays a large role in this course. Some instructors choose to allow the use of numeric integration via a calculator throughout the course while prohibiting the use of a calculator of any type in the chapter on techniques of integration.

### Technology

All students should be expected to have a graphing calculator and be encouraged to use it effectively. Instructors may take advantage of the availability of various software packages such as *Mathematica* and MATLAB for both demonstration purposes and student assignments. Students who transfer to four-year schools may need some experience with these packages. However, since the needs of the students will vary, mastery of the software should not be expected. Possible topics for software use are graphing solids of revolution, graphing of parametric and polar equations, graphical demonstrations of convergence of series, radius of convergence for a series and the approximation of functions with a series. Some instructors also have the students compare the results of a computer solution for an indefinite integral with the results of a hand derivation.

## Math 101C Calculus III

### Teaching the Course

This course is designed for students majoring in math, engineering and the physical sciences. As compared to Calculus I and II, there will be fewer students majoring in Business and the Biological Sciences. Students will see many three-dimensional problems, including the visualization of intersecting quadratic surfaces. This visualization is often difficult for students but is essential for the proper set up of double and triple integrals. Smith and Minton's *Calculus* includes parametric surfaces to a greater extent than in some other books.

Students will also see many applications that would typically be found in a physics course, including projectile motion and static equilibrium. If a student does not have any background in physics, that student will need to work a little bit harder in the related sections.

### Technology

Instructors should take advantage of the availability of various software packages such as *Mathematica* and MATLAB for both demonstration purposes and student assignments. Students who transfer to four-year schools will need some experience with these packages. However, since the needs of the students will vary, mastery of the software should not be expected. Possible topics for software use are graphing three-dimensional parametric curves and surfaces, quadratic surfaces, and surfaces in a spherical or cylindrical coordinate system.

## Math 103 Linear Algebra

### Teaching the Course

This course is designed for students majoring in math, computer science, engineering and the physical sciences. In particular, this is a transition course for students since it is the first college course with an emphasis on proofs.

### Technology

Many graphing calculators have the commands to perform matrix reduction to reduced row-echelon form. Some of the calculators can also determine the eigenvalues and eigenvectors for a matrix. The software package MATLAB is one of the better software choices for use in this course. Traffic models, Leontief economic models, and Markov chains provide good applications with larger scale matrices.

## Math 104 Differential Equations

### Teaching the Course

This course is designed for students majoring in math, engineering and the physical sciences. While the emphasis should be placed on the applications of differential equations, students should be expected to do a certain number of proofs. Specifically, proofs of some of the theorems within the chapter on Laplace transforms should be well within the grasp of the students.

Students majoring in Electrical Engineering will need a thorough understanding of Laplace transforms and second-order linear differential equations. Students majoring in mechanical engineering will benefit from an introductory look at the heat equation.

### Technology

Instructors should take advantage of the availability of various software packages such as *Mathematica* and MATLAB for both demonstration purposes and student assignments. Students who transfer to four-year schools will need some experience with these packages. However, since the needs of the students will vary, mastery of the software should not be expected. Possible topics for software use are drawing slope fields, drawing solutions to problems not solvable by "elementary" methods, drawing Fourier series, computing solution to messy undetermined coefficient problems.

## Math 111 Introduction to MATLAB

### Teaching the Course

This course is designed for students majoring in math, computer science, engineering and the physical sciences. The intent of the course is for students to become proficient in using the software package MATLAB.

### Technology

Mastery of a professional package like MATLAB is unlikely in an introductory course. However, by the end of the course, students should become comfortable writing computer code. They should also be comfortable reading sample code from the documentation and public web sites, and while providing credit to these sources, adapt the code to their own use.

## Math 151 Algebra I

### Teaching the Course

This is a first course in elementary algebra. While some students have never had a course in algebra, many have previously taken a similar course but are repeating the course for a variety of reasons. Many students have difficulty with concepts from arithmetic, especially operations with fractions and percentages. Nearly all students have difficulty with applications. For some students, diagnosed learning disabilities and/or extremely low self confidence provide a large barrier to success

Many of the students in the course have problems with keeping up with the material. Some of the reasons are poor study skills, unfamiliarity with the workload of a college course, a heavy load of commitments outside of the classroom (work, family, etc.), and bad experiences in previous courses leading to a fear of math. In addition, some students feel comfortable with the first chapter of material and this results in a drop in attendance and/or attention to the course. When the harder material arises, these students find themselves in a poor position to continue with the course.

All of these factors makes this a challenging course to teach. The instructor will need to provide constant encouragement and motivation to the less skilled students and, at the same time, hold the attention and interest of those students who remember a majority of the material but are being forced to repeat the course.

### Technology

The students in the course will need a standard calculator. Most of the full-time faculty encourage the use of a calculator, rather than a calculator that comes with a cell phone or PDA.

The courseware package MyMathLab is available for use in this course. For further information, contact the Course Coordinator.

## Math 151A/B Algebra I

- Book
- Course Coordinator
- Official Course Outline Math 151A (PDF)
- Official Course Outline Math 151B (PDF)
- Sample Exams

### Teaching the Course

These two courses combined have the same content as Math 151. However, since the material is spread over two semesters, the pace of the course is slower.

## Math 151A/B Self-paced Algebra I

### Teaching the Course

Some sections of Math 151A/B are taught in a self-paced format. Students are expected to come to class on a regular basis. However, instead of a lecture/discussion methodology, students work independently on both paper and computers. The instructor and (normally) a student tutor will walk around the room providing individual assistance. It is important for the instructor to ensure that each and every student is making consistent progress through the material. A lack of attendance by a student is often a sign that a student is no longer devoting the appropriate amount of attention to the course.

For complete information about the use of software and other details of the course, please contact the Course Coordinator.

## Math 152 Algebra II

### Teaching the Course

This is a second course in elementary algebra. The course differs from Math 152 in the target audience. Math 152 is designed for students who will take courses at the level of trigonometry or higher. Math 153 is designed for students whose terminal math course is Math 156 (Math for Liberal Arts) or Math 159 (Statistics). While Math 152 and Math 153 cover the same broad topics, the depth of the coverage in Math 152 substantially greater than that of Math 153.

While most students have a higher math competency than those students in Math 151, the same issues regarding study skills, knowledge of prerequisite material, outside demands, etc. play a strong role in this course. In addition, some students who have successfully passed both a beginning algebra course and a placement test will have difficulty remembering prerequisite material in a timely fashion.

### Technology

The students in the course will need a scientific calculator for use with exponents and logarithms.

The courseware package MyMathLab is available for use in this course. For further information, contact the Course Coordinator.

## Math 152A/B Algebra II

- Book
- Course Coordinator
- Official Course Outline Math 152A (PDF)
- Official Course Outline Math 152B (PDF)
- Sample Exams

### Teaching the Course

These two courses combined have the same content as Math 152. However, since the material is spread over two semesters, the pace of the course is slower.

## Math 152A/B Self-paced Algebra II

### Teaching the Course

Some sections of Math 152A/B are taught in a self-paced format. Students are expected to come to class on a regular basis. However, instead of a lecture/discussion methodology, students work independently on both paper and computers. The instructor and (normally) a student tutor will walk around the room providing individual assistance. It is important for the instructor to ensure that each and every student is making consistent progress through the material. A lack of attendance by a student is often a sign that a student is no longer devoting the appropriate amount of attention to the course.

For complete information about the use of software and other details of the course, please contact the Course Coordinator.

## Math 153 Intermediate Algebra

### Teaching the Course

This is a second course in elementary algebra. The course differs from Math 152 in the target audience. Math 152 is designed for students who will take courses at the level of trigonometry or higher. Math 153 is designed for students whose terminal math course is Math 156 (Math for Liberal Arts) or Math 159 (Statistics). While Math 152 and Math 153 cover the same broad topics, the depth of the coverage in Math 153 is substantially reduced from that of Math 152.

While most students have a higher math competency than those students in Math 151, the same issues regarding study skills, knowledge of prerequisite material, outside demands, etc. play a strong role in this course. In addition, some students who have successfully passed both a beginning algebra course and a placement test will have difficulty remembering prerequisite material in a timely fashion.

### Technology

The students in the course will need a scientific calculator for use with exponents and logarithms.

## Math 153 Self-paced Intermediate Algebra

### Teaching the Course

Some sections of Math 153 are taught in a self-paced format. Students are expected to come to class on a regular basis. However, instead of a lecture/discussion methodology, students work independently on both paper and computers. The instructor and (normally) a student tutor will walk around the room providing individual assistance. It is important for the instructor to ensure that each and every student is making consistent progress through the material. A lack of attendance by a student is often a sign that a student is no longer devoting the appropriate amount of attention to the course.

For complete information about the use of software and other details of the course, please contact the Course Coordinator.

## Math 155 Math for the Associate Degree

### Teaching the Course

This course is designed for students who plan on completing an Associate's degree but not pursuing any other degree with a higher math requirement. The intent of the course is to promote interest and enjoyment in math. Faculty are encouraged to have the students create projects that will involve the use of mathematics and present these projects to the class.

This course differs from Math 156 in that this course is non-transferable to a four-year school and that it does not satisfy the CSU math graduation requirement. In addition, the math content of the students is at a lower level than that of Math 156.

### Technology

Instructors may choose to use software to demonstrate the beauty inherent in mathematics. There are numerous web sites devoted to the topics such as fractals, tiling and artistic perspective. There are also many sources of historical information including numeration systems for other cultures. The students should be able to use a calculator to compute exponents.

## Math 156 Math for the Liberal Arts

### Teaching the Course

This course is designed for students who plan on completing an Associate's degree or a Bachelor's degree. The intent of the course is to promote interest and enjoyment in math. Faculty are encouraged to have the students create projects that will involve the use of mathematics and present these projects to the class.

This course differs from Math 155 in that this course is transferable to many four-year schools and that it satisfies the CSU math graduation requirement. In addition, the math content of the students is at a higher level than that of Math 155.

### Technology

Instructors may choose to use software to demonstrate the beauty inherent in mathematics. There are numerous web sites devoted to the topics such as fractals, tiling and artistic perspective. There are also many sources of historical information including numeration systems for other cultures. The students should be able to use a calculator to compute exponents and logarithms.

## Math 158

- Course Coordinator
- Official Course Outline

## Math 159 Elements of Statistics and Probability

### Teaching the Course

This course is the introductory course for Statistics. In addition to introducing the concepts of statistics and probability, instructors should provide students with a motivation of how these topics affect daily decisions. As much as possible, students should work with real data, and should focus on the conclusions of the statistical analysis rather than the analysis itself.

### Technology

Due to articulation agreements with four-year schools, instructors must incorporate the use of technology throughout this course. Some instructors use Microsoft Excel because it is readily available. Some instructors use the Texas Instruments calculators (models TI-83/84) because of their ease of use and portability. Other instructors use special purpose statistics software.

### Other Material

There is a nice java applet that shows how α, β, type I and type II errors relate to each other for hypothesis tests at:

intuitor.com/statistics/CurveApplet.html

## Math 167 Calculus for Business and Social Sciences

### Teaching the Course

This course is a survey course in Calculus and does not have trigonometry as a prerequisite. While the students are generally highly motivated, their math skills are not at a level of the typical student entering Math 101A. Instructors should emphasize the concepts and applications of Calculus. The students should be provided with an informal motivation for each new topic.

Note that all students majoring in business, accounting, etc. who plan on transferring to a four-year school should be sure this course is accepted by the four-year school. Many universities, including some campuses of the University of California require Math 101A. Students should check with their counselor and/or with www.assist.org.

### Technology

The most commonly used technology for this course are the Texas Instrument TI-83/84 calculators. Students can be directed to the Calculator Help page for detailed instructions on these and other models.

Some instructors have used *Mathematica* and/or Microsoft *Excel* for classroom demonstrations. Assignments for the students using these packages are appropriate but certainly not an expectation. However, since the needs of the students will vary, mastery of the software should not be expected.

## Math 181 Trigonometry

### Teaching the Course

Students taking this course typically have problems in a few areas. Those students who are unfamiliar with elementary geometry will benefit from an brief as-needed review of the alternate interior angle theorem and the vertical angle theorem. Students will be using these theorems when solving word problems, particular navigation problems. Students who are uncomfortable working with fractions will have difficulty finding all the important points for the graph of *y* = sin (3*x* - 5π/12). Finally, students seem very reticent about memorizing the special trig values, such as cos (π/6). Because the students do not memorize these values, they have a very difficult time solving trig equations.

### Technology

The most commonly used technology for this course is the Texas Instrument TI-83/84 calculator. Students can be directed tothe Calculator Help page for detailed instructions on these and other models.

## Math 188 Precalculus

### Teaching the Course

While some students consider this course simply a review of algebra and trigonometry, the course content is can be misleading. Problems in areas such as factoring are often substantially more difficult than found in the previous courses. Coverage of the material on functions is at a higher level and of greater depth. Some topics, such as the graphing of rational functions, are not normally seen in previous courses. In addition, the number of topics requires that the course proceed quickly.

Instructors teaching the course for the first time should be aware that the textbook has some tricky problems that require a bit of ingenuity.

Since the course is designed for student who will proceed to Math 101A, instructors should concentrate on skills and concepts that students will find useful in subsequent courses. In particular, word problems should play an important role on both the homework and the exams.

### Technology

The most commonly used technology for this course is the Texas Instrument TI-83/84 calculator. Students can be directed tothe Calculator Help page for detailed instructions on these and other models. Students should be expected to effectively use a graphing calculator. Topics to include are determining solutions to equations graphically and determining appropriate graphing windows. Students should also be aware that the use of a graphing calculator complements (rather than substitutes for) their own mathematical skills. For example, students should be aware that the graph of a fifth-order polynomial always has at least one root, despite what the graph on their calculator may currently show.

## Math 190 Basic Mathematics

### Official Study Guide

The student study guide for this text is available: MATH-190 Student Study Guide (PDF).

### Teaching the Course

This is a course in arithmetic. Some students are taking the course to refresh lost skills and other are trying to gain skills that have eluded them during elementary and high school. For some students, diagnosed learning disabilities and/or extremely low self confidence provide a large barrier to success.

Many of the students in the course have problems with keeping up with the material. Some of the reasons are poor study skills, unfamiliarity with the workload of a college course, a heavy load of commitments outside of the classroom (work, family, etc.), and bad experiences in previous courses leading to a fear of math. In addition, some students feel comfortable with the first chapter of material and this results in a drop in attendance and/or attention to the course. When the harder material arises, these students find themselves in a poor position to continue with the course.

All of these factors makes this a challenging course to teach. The instructor will need to provide constant encouragement and motivation to the less skilled students and, at the same time, hold the attention and interest of those students who remember a majority of the material but are being forced to repeat the course.

### Technology

The students in the course will need a standard calculator. Most of the full-time faculty encourage the use of a calculator, rather than a calculator that comes with a cell phone or PDA.

There is a software package that allows students to practice randomly generated problems problems. This software is distributed with the textbook and is available from the Math Learning Center.

## Math 191 Prealgebra

### Teaching the Course

See Math 190.

## Math 192 Basic Math and Prealgebra

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