A Few Thoughts on Digital Homework Assignments

Digital homework assignments within digits and HMH A-G-A provide value-added supports to students such as instant feedback and on-demand help. No print textbook has ever been able to provide this kind of just-in-time support, so that is a benefit of using technology as a tool for learning mathematics.

When interacting with a digital interface, it is common for students to neglect paper and pencil and perform (or attempt) all calculations in their head. While the digital interface can entice students to forget about paper and pencil and diligently documenting their thinking and processing, we must insist this practice remains a core component of learning, doing, and practicing mathematics. Students should always record their mathematical thinking and processing in some form of a math notebook, regardless of whether it’s scored for completion or accuracy. If you are thinking digital assignments will save you (the teacher) time by not having to collect, grade, or review homework altogether, this is a misconception. An unfortunate possibility of digital homework is that students may end up learning more about “gaming” the algorithm behind such assignments and learning to cheat on assignments vs. learning and practicing mathematics as intended. Also, the help features can become a significant crutch for students, essentially walking them through similar problems where only the numeric values are different and the key becomes to learn the structure of the problem and where to put the numbers. In this case, students could score 100% on assignments without knowing any mathematics whatsoever. That’s why there must be a balance with paper-pencil and digital interface to collect accurate formative assessment data. In addition, do digital assignments provide the types of items that are worth students’ time and effort? Are the items mere rote practice exercises requiring low-level recall or simple procedures? Do these items allow students to apply the Standards for Mathematical Practice (particularly SMPs #1 and #3)?

So, why insist on having students write down their work and processing with digital assignments?

  • It provides a complete written record of exercises and tasks that can be referenced later. Digital platforms, at best, only archive the answers submitted, whereas a complete written record can be referenced at anytime with a useful amount of detail.
  • It allows for error analysis and precise feedback, whether scored for completion or accuracy. Digital platforms will only report right or wrong answers and cannot diagnose where errors occurred or the potential misconceptions that may exist.
  • Benefits of writing for long-term comprehension. Even though this is referring to note-taking through writing vs. on a laptop, the same ideas can transfer to mathematics with the value of writing things down and the mental processing involved.
  • Opportunities for metacognition, self-assessment, and reflection. Being able to review work, identify strengths and weaknesses, and reflect on next steps are much more viable with written work where annotations and editing are possible.
  • A written record makes thinking transparent (especially for complex tasks and problems). Rote practice exercises can be done without needing to precisely record all steps and thinking, but complex tasks and problems that require analysis, reasoning, and synthesis require some recording of steps.

Overall, digital homework assignments are not bad, as there are valuable benefits for students as they complete the exercises. Perhaps the most limiting aspect of digital assignments are the item types that must be used for the digital scoring. These items may pose multi-step problems that hint at using the Standards for Mathematical Practice and actually “doing mathematics,” (see the Mathematical Task Analysis Guide by Stein, Smith, Henningsen, & Silver, 2000) but the digital interface can reduce the student experience to multiple choice, filling-in-the-blanks, selecting from drop-down menus, or simply being asked to enter a numeric answer. In some cases, students may be asked to complete a specific line of thinking and reasoning for a multi-step item that may feel forced or inauthentic, not honoring alternative strategies or respecting how the student would approach and solve the problem. When the goal is for students to engage in multi-step items that require perseverance, problem-solving, justification, and applications of concepts (hopefully students have the opportunity to engage in these kinds of tasks regularly), simply give these tasks in a paper-pencil format where students must construct their own mathematical reasoning and communication of ideas. The resulting mathematical discourse in the classroom will be much more valuable and meaningful to everyone than viewing a data dashboard of right and wrong responses.

(Want more? David Wees shared some additional thoughts in a recent blog post.)

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