
One write way to student success in mathematics

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Failing a course twice can put students in a difficult situation. Typically, the course is required and a third attempt requires special approval. However, this provides an opportunity to snatch success from the jaws of failure.
In our resource-limited urban public university, we鈥檇 like to provide all that better-resourced universities can afford. We cannot. But there鈥檚 opportunity to level the playing field.
In my role as department chair, I developed a structure for a two-strikes approach to turning course failure into a pass. Guiding students to articulate challenges and reformulate approaches, we build an improvement plan during a one-on-one meeting and a letter-writing task. The process, applicable beyond coursework, emphasises personal conversations, quality writing and reflective exercises that promote academic commitment and achievement.
Reframing failure as skill-building opportunity
The first step is a face-to-face conversation with the student. Verbal delivery is easy and succinct. Without using the word, I ask what brought past failure and what might bring future success. Is a teacher to blame? I sometimes point to Steven Zucker鈥檚 article 鈥鈥: most college learning responsibility rests with the student; most learning takes place outside the classroom. This is general, inspiring reading, not an easy fix. Responses such as 鈥淚 don鈥檛 need any more maths鈥, or 鈥淭his course is holding me back from鈥︹, or 鈥淚 was always bad at maths鈥 often lead me to bring up George Orwell鈥檚 1984 and its .
- Spotlight: How to fail well
- Decolonising learning through access to primary sources
- Why students are best placed to help students understand feedback
I suggest reframings, which might read: 鈥淣o additional maths courses are required for my programme, though taking such may strengthen my background鈥, 鈥淐ompleting this class rounds out my programme. It鈥檚 required for my degree, with good reason鈥 and 鈥淚 may even become good at maths; think of maths as a new strength鈥.
I don鈥檛 post general suggestions online (on, say, web pages on course repeat policy), avoiding being prescriptive. I vary meeting themes. The writing guidelines are met without resistance, often with a smile.
Writing a path to success
The homework assignment comes next. Students write a request letter, outlining a path to success. I provide instructions, encourage hand note-taking and discourage electronics. 鈥淭hese are instructions, not dictation.鈥 It should be made clear that quality writing is expected 鈥 English-paper grade, yet using the student鈥檚 own words. Plain-text format is required 鈥 no attachments, no graphics, colours or fonts. This emphasises word choice and gains logistic advantages:
I could express my thoughts鈥ith a limited set of words and grammatical structures, as long as I combined them effectively and linked them together in a skilful manner. Haruki Murakami
The formatting requirement is always initially accepted, although submission in non-compliant form often follows. Attention to detail is important for all classes. Deviation from instructions is acceptable, but only with clear rationale. Alternatives are negotiable.
Writing guidelines follow. For clarity, a formal sentence is expected: 鈥淚 request鈥upport for...鈥 This contradicts in your own words; no one objects. Next, when and with whom did you take the class? Everyone remembers when; many forget whom. 鈥淟ook it up.鈥 Detailed recall helps later.
Failure analysis comes next. Were first-strike lessons insufficient for second-attempt success? The student should list reforms, initiatives or new ideas for success. I offer suggestions, leveraging campus resources: tutoring, office hours, study groups鈥 Some students with disabilities acknowledge special resources yet untapped; others learn of these for the first time. I encourage students to add ideas; friends and family are mentioned. Students鈥 ideas emanating from new directions (job, relatives, commuting) signal a successful conversation.
Specific study days/hours are reserved for this class and detailed in the letter. Not 鈥渢wo hours on Tuesday鈥; instead 鈥淭uesdays, 2:30-4:30鈥 reinforces the need to devote more outside than in-class time. (A 2:1 ratio is standard.) Students acknowledge that study-time allocations might have been meagre in the past. Length of time is not the only factor 鈥 time must be well spent (and instructor guidance is particularly valuable for that). Uncertain work schedules are mentioned. Then I suggest making a best guess, committing to later compensations, with no net loss. This section of the request letter is often weak. Careful re-reading of instructions and attention to detail yield improved revisions and will help future coursework. (Some write more than requested, including, for example, dog-walking schedules.)
Writing skill shortcomings emerge. Usage weaknesses appear among non-natives (鈥済rab some lunch鈥) and natives (鈥渞eason being as鈥). I point out that good mathematics and good writing go hand in hand, linking to the writing centre.
Other considerations in the process
- What if a study schedule is made up? This rarely happens, I believe. Questions and remarks suggest sincere intentions. Why is whole-plan specificity important? Making choices is psychologically taxing. Weekly study-time decisions can be consuming.
- Weakness of fixed schedules? Benedict Carey鈥檚 says that varying study venues helps. Why not vary time? Timing will vary, best intentions notwithstanding. Not to worry 鈥 there鈥檚 value in planning itself.
- Dividends are the good things emanating from course success. Sometimes a brief discussion of dividend is needed. The (ironic) post-Soviet peace dividend is recalled. Students go beyond grades and requirements in articulating success dividends 鈥 learning readiness or not needing to outsource mathematics in the workplace, for example. Envisioning dividends increases course value buy-in, driving success. Alongside positive dividends are negatives. Imagine a third strike. Envisioning negatives has greater impact than positives. Asymmetry can be leveraged.
- Priorities and responsibilities: During repeat, what鈥檚 the commitment load? Where does this course fit in? Excess specificity is common here. Don鈥檛 say 鈥淭aking my cousin to dialysis鈥; say 鈥淔amily responsibilities.鈥 Course priority need not be tops, but it should be high. Totality of responsibilities is also important. Is it right sized? Can we realistically expect to meet all expectations? Have these aspects been considered?
- Obstacles: What might impede success? How to circumvent them? We digress on obstacle. I cite a student offered 80 work hours in one week 鈥 good money, but school suffers. A prior commitment of 25 work hours makes it easier to say 鈥淭hanks; opportunity appreciated but I made a commitment鈥︹ Otherwise, resistance is hard.
This process seems longwinded when it鈥檚 written down; verbal delivery can be rapid. Successful requests are often short. When strong portions are present, with no red flags (poor writing, instructor blaming, dismissing course value, not following instructions), review is rapid. Feedback yields adequate revision in most other cases.
Mindset and positive (and contrapositive) psychology influence the process. Instruction copies are not provided, placing emphasis on conversation. There鈥檚 no script; delivery varies, guided by real-time student reactions.
Outcome statistics are not available. Negative recountings never arrive, positives sometimes:
Dear Professor, You supported my third retake request. I was thrilled鈥 I earned a [high grade]鈥 The appeal letter I wrote鈥helped tremendously!
Eric L. Grinberg is a professor in the department of mathematics at the University of Massachusetts Boston.
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