What follows are ten mathematics instructional practices (MIPs) are meant to capture the nuances of the majority of mathematics instruction for the first two years of college mathematics.

- Lecture
- Collaborative Lecture
- Cooperative Learning
- Inquiry-based Learning
- Emphasis on Application Problems
- Emphasis on Project-based Learning
- Emphasis on Multiple Representations
- Emphasis on Communication Skills
- Mastery Learning
- Emphasis on Formative Assessment

These MIPs are not part of my Ph.D. dissertation research, they are just something I needed to do in order to focus my literature review on a narrow and clearly defined set of instructional practices for mathematics. Thank you to everyone who gave me feedback in the last two days – it was vital to developing a comprehensive list of practices.

I am permanently posting the list (with descriptions and illustrative examples) under the Resources tab on this website (go here). You can also print the full list and research notes from the feedback surveys in the last two days (here). I only ask that if you use these as part of a study, paper, or presentation, that you use the proper citation (or if it is digital, link back to the site).

Please note that the use of technology for instruction is not its own category on the MIP list (ironic, I know). However, technology is used as part of the implementation of various instructional strategies. Emphasis on technology itself is not an instructional strategy that can be easily summarized and is left to future exploration. The practices in the MIP are also meant to describe the nuances of teaching face-to-face (and not online). The nuances of mathematics instructional practices for online courses will be left for future research. It is important to first establish a baseline for MIP that occurs in face-to-face instruction.

Remember, no instructor will fall distinctly into any one category. All of us will use a mix of each of these practices, to varying degrees. In the final instrument to measure instructional practice, you would be asked to what extent you use each strategy in your courses (at a specific level of mathematics) and you would respond on a scale. Likewise, many activities that you do in the classroom may span more than one category of instruction. The intent of the categories is to lend description to different nuances of instructional practice in mathematics.

If you would like to publish this list as part of a scholarly work, or you have suggestions for where to seek publishing of the MIPs and the development of the list, please let me know. I hope it will be useful as a way to focus the language of the research in mathematics instructional practices with a common language.

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