- Why Create Different Paths?
- A Typical Day
- Planning a Redesign
- Math Literacy Goals and Objectives
- Best Practices
Considerations for Implementing a Redesign
In order to get the most support and buy-in from administrators and other units on campus, launch an informational/PR campaign for your math literacy course well in advance.
- Clarify what concerns the department wants to address in its algebra sequence. Research options and present them to your department.
- Emphasize that this course does not water down expectations—it offers a rigorous and more appropriate alternative for students who aren’t required to take college algebra.
- Point out that by creating a second track, the traditional track can be adjusted to better address the needs of students who are required to take college algebra.
Instructor Buy-in and Training
- Offer informational sessions so instructors can decide if they can get excited about about this course, and then offer training sessions for instructors who decide to teach it.
- Training should address both content and pedagogy. If you have any sections of the course in progress, classroom observations are very helpful. This experience alleviates many of the concerns about the group pedagogy.
- There is much pressure on school administrators to decrease student time in remedial coursework, and time to completion of the first college-level math course.
- Emphasize that this course shortens the developmental course sequence, and better prepares students for their required college-level general education math course.
- This is one of the most important things to do, since most students have direct contact with advisers first.
- Work very closely with advisers to make sure they understand who should take this course.
- Make sure advisers understand the pedagogy and goals of the course, so they can explain the course expectations to students.
- Make sure advisers understand why this is such a great opportunity for students—some may not be familiar with retention rates in traditional developmental math courses, so they may not understand why a second path is a good option.
- Get advisers excited about this course by emphasizing the benefits, including less time in developmental coursework.
Informing other Departments
- Other departments that use developmental algebra courses as prerequisites to their own courses or programs will need to decide whether they want to use this course to satisfy any of their requirements.
- Provide each department with a topic and pedagogy comparison between this course and those they currently require
- Have a representative from your department be available to discuss whether this course might be appropriate.
Marketing to Students
- Make sure students know in advance that this option is coming, so they can determine how it impacts their course path.
- Advertise around campus, and in existing developmental courses. You can use flyers, social media, and other avenues to share the information with students.
- Encourage students to see an adviser to determine which course path is best for them.
Details, Details, Details
- Don’t forget details like changes to the course catalog. In addition to a new course description, you will need to change the prerequisite language in some of your college-level courses. Provide this prerequisite language to other departments who will need it for their own program and course descriptions.
- Work with the scheduling unit on your campus to iron out details with class scheduling. This course works best with class periods longer than the traditional 50-minute period.
General Goals and Objectives for Mathematical Literacy
- Provide a preparatory course for college-level general education mathematics and statistics courses that includes content that is more relevant for this path.
- All topics presented in context
- Focus on numeracy, functions, and modeling
- In addition to algebra topics, promote data literacy
- Incorporate reading, writing, and technology
- Less by-hand symbolic manipulation, more critical thinking and problem solving
- Incorporate a pedagogy that promotes contextual problem solving and critical thinking
- Group-based pedagogy, less use of lecture
- Basic skills reinforced with online homework system outside of class
- In class, work on conceptual understanding and problem solving: look at real data, explore patterns, create models, solve problems, have fun
- Increase student engagement among non-STEM students (they could even like it so much they decide to go STEM!)
- Increase retention in developmental mathematics courses
- Reduce the number of developmental courses students need to take—replace beginning and intermediate algebra with one course for this path
- Reduce time to completion of the first college-level mathematics course
- Reduce the amount of financial aid used up at the developmental level
All presented in context
- Numerical/Algebraic Skills and Reasoning. Students should be able to: use inductive reasoning to form conjectures; use deductive reasoning to confirm conjectures; use estimation appropriately; verbally communicate results and reasoning; perform arithmetic operations and unit conversions; use scientific notation; identify linear, quadratic, and exponential patterns; simplify and evaluate algebraic expressions; use the zeros of a polynomial to factor; solve linear equations numerically, algebraically, and graphically.
- Data Literacy. Students should be able to: create and interpret visual representations of data; read, interpret, and make decisions based upon data from graphical displays, such as line graphs, pie charts, bar graphs, and scatterplots; calculate mean, median, and mode; use linear and exponential curve fitting to model data relationships and analyze correlation; discuss misrepresentations and misinterpretations of data in the media.
- Functions and Modeling. Students should be able to: identify properties of a function using the graph; understand the concepts of linear and exponential growth; interpret slope of a line as a constant rate of change; represent linear, quadratic, and exponential functions graphically; identify whether a given situation is best modeled by a linear, quadratic, or exponential function; write a linear function to model an application; use linear and exponential curve fitting to model and analyze a situation or relationship; use direct and inverse variation to model and analyze a situation or relationship.
- Equations and Modeling. Students should be able to: use proportional reasoning to model and analyze a situation or relationship; apply the Pythagorean theorem and other geometry concepts to model a situation or relationship; use systems of equations to model a situation or relationship.
- Discussions about study skills, traits of a successful person, and personal responsibility incorporated throughout.
Best Practices for your Math Literacy Course
Classroom Management and Group Work
- The classroom should be conducive to group work, with tables rather than individual desks.
- Don’t help too soon. Know when to step back and give the students time to wrestle with a question.
- On the other hand, don’t wait for students to raise their hands for help. Move around the room, listening to their conversations and asking them questions about what they are working on and how they are approaching it.
- Group work is an important part of the course pedagogy. Not all students come into the course liking group work, but most find it to be valuable once they get used to it. Explain that the group dynamic in this course is different from what they may have experienced in the past.
- Group management is a fine art, and it does take some time and thought. For the instructor, it also requires that you accept that you will not always be in control. Trust the process. You might have a day that feels like a flop, but you will have more days that are fun and rewarding.
- It works best if you change the groups each unit. The longer a group is together, the more the students start to socialize and get off-task.
- You will not always get it right. Some groups will work better than others, and you learn as you go.
- For graded group work, build in some sort of accountability. For example, have students grade each other for effort and contribution to the project, and include this as part of their grade. This helps hard-working students to feel like they are not giving a free ride to students who do not participate.
This class is very different from what students are used to, so there is some management of student expectations that is necessary. A First Day of Class presentation is available for instructors to introduce students to the course.
- This course is different from traditional algebra classes. Everything they will learn has a purpose and a use. While they won’t use every topic in their own jobs, someone (who is a real person, and not a mathematician or engineer) does.
- This class may not do all the abstract algebraic manipulation, but it is quite challenging in other ways. Students will be required to actively engage with the math, and think about it in deeper ways than they are used to.
- Collaboration is not only an important life skill, but it is also an excellent learning tool. You will have to be able to work with people you don’t get along with. You will also learn a lot by asking questions, answering questions, and working together.
- This is a technological world. Employers expect their employees to be familiar with technology, and to be able to use it in a productive way. The technology assignments will prepare students for this, while also reinforcing some key ideas.
- Math is not about memorization—it is about critical thinking, problem solving, interpretation, and much more.
- Part of the goal of this course is to learn how to grapple with hard problems that you don’t immediately know how to do. Knowing how to “struggle productively” with a problem until you figure it out is a skill that you have to learn, and to learn it you have to practice it—that is what we will do in this course.
A detailed instructor overview of best practices for using Pathways in your math literacy course is available.