Acceleration Through Vertical Redesign:
Developmental and Intermediate Algebra
Increase success rate in College Algebra.
Premise of the Project
All human beings are hardwired to do mathematics or can learn basic mathematics.
We wanted to create an environment more conducive to learning. We also wanted to share our joy of mathematics. We wrote a text for the course that would bring to the reader a view of mathematics as art, logic, and a way of thinking. We also wanted to expose the reader to problem-solving skills often missed in traditional developmental mathematics courses.
Key Features of the Project
- Modular learning. Content is divided into five modules. View the Developmental and intermediate Algebra Textbook to see the redesigned content. Text material is copyrighted to the authors but can be used freely for educational purposes only.
- Mastery-based learning. Mastery of 80% or higher is expected in each module.
- Flipped Classroom. YouTube lectures are embedded in the e-text.
- Visual interpretations and solutions. We make extensive use of visual representation using strip diagrams and other techniques.
- Insight into higher-level mathematics. While building a deep understanding of K-12 mathematics, we also take several opportunities to provide higher-level insights.
- Importance placed on mathematical reasoning. We try to teach students how to articulate valid mathematical reasoning and constantly engage in knowing why they did what they did.
- Increasing student comfort making mistakes. We try to create an atmosphere in which students are more comfortable and willing to risk mistakes during in-class discussions to maximize learning.
- ALEKS. This project makes use of the ALEKS program which efficiently covers the drill-and-skill that is essential to succeed in mathematics. Visit www.aleks.com for more information on this artificially intelligent program.
- Savings of time and money. Aside from the free e-text, the newly developed course covers material from developmental (Mat 091) and intermediate algebra (Mat 105) in one semester with 4 credits (compared to the typical two 3-credit courses over two semesters).
The newly developed course is Mat 103 (previously labeled as a Mat 091/105 combined course). Mat 103 is taught as a flipped course (in which students watch lectures at home and ask questions and receive practice in the classroom). We wanted the lectures and e-text to be free and easily available to anyone who wants to learn. The book presents content in a nonstandard sequence to reveal connections among many different topics. The authors also provide a Module Zero that applies mindfulness techniques and study skills to help those who might have anxiety related to the learning of mathematics. We believe that anyone can learn mathematics and that it is just a matter of patience and hard work. We believe that if students could review basic mathematics, then most can place out of developmental mathematics courses upon arriving to college.
Below is the structure of the material presented in the e-text in five modules.
Summary Data (2011-2012)
Based on data from over 300 students in fall 2011 and spring 2012, Mat 105 course grades were significantly higher when students took the combined Mat 091/105 course compared to the traditional Mat 091 and 105 two-course sequence (see figure below; A = 4.0, B = 3.0, etc…). Based on data from over 80 students in Mat 110 in spring 2012, Mat 110 course grades were significantly higher when students had come from the combined Mat 091/105 course compared to the traditional Mat 091 and 105 two-course sequence.
Since the project began, this course has been piloted successfully at other UW campuses (including UW-Milwaukee). Success rates (of C or better) have ranged from approximately 70% to 84%. Students and instructors have contributed to the project through feedback and suggestions. Many others have also contributed in a variety of ways. (See the e-text for acknowledgments.)
Parts of this project were partially funded by a COBE grant in 2011 and 2012.