math assignment
Formal Write Up #2
In the last few weeks we have introduced several differentiation rules:
● Constant Multiple Rule ● Sum Rule ● Power Rule ● Derivative of Exponential Functions Rule ● Chain Rule ● Product Rule ● Quotient Rule
Part 1: The first task of this formal write up is to reflect on and summarize those rules. Each rule
should have its own separate mini-summary that includes the following:
● A full statement of the rule.
○ E.g. “The constant multiple rule states that if is a constant and is a functionc (x)f
with a derivative, then ”c (x) c f(x)ddx · f = · d dx
● A description of the rule in colloquial terms
○ E.g. “This means that if a differentiable function is scaled by a factor of , then thec
rate of change of that function at any moment is also scaled by a factor of ”c
● A complete and narrated example showing the rule being used.
○ It may help to think of this as explaining an application of the rule step-by-step to
another student.
● A reflection on your understanding of the rule. This should include, at a minimum, answers
to the following:
○ What do you find difficult about this rule?
○ What do you find easy about this rule?
○ How might someone misapply this rule? Give an example, explain why your example
is a misapplication, and why someone might believe the misapplication is valid.
○ Can you explain why the rule works? Attempt a short justification. Discuss how
convincing you think your justification is and why.
Part 2: For this part, choose one of the rules and give a thorough explanation of why the rule works in general. Your explanation should be able to support a new calculus student in fully understanding why the rule works. Include visual representations (graphs, pictures, etc) and worked examples that purposefully support your argument for why the rule works in general. You may want to build off of parts of your mini-summary for whichever rule you choose.
General Rubric
Part 1: For each differentiation rule summary, you will be assigned 0-3 points for each bullet point listed:
● A full statement of the rule. ● A description of the rule in colloquial terms ● A complete and narrated example showing the rule being used. ● A reflection on the rule.
3 points: Clear, articulate and complete response that correctly addresses each component of the prompt. 2 points: A few important details are missing, but the overall quality is good. 1 point: Many important details are missing, but an effort was made to answer the prompt 0 points: No attempt All together, Part 1 will be out of 84 points (7 differentiation rules 4 bullet points 3 points per× × bullet point)
Part 2: This part will be out of 16 points
● Purposeful use of visual representations (0-4 points) ○ 4pts - visual representations are used correctly and meaningfully as part of the
exposition on why the rule works in general ○ 3pts - visual representations are used as part of the exposition but there are minor
flaws ○ 2pts - visual representations are present but not leveraged as part of the exposition
or have major flaws ○ 1pts - any other attempt ○ 0 pts - no visual representations present.
● Purposeful use of worked examples (0-4 points) ○ Same as above, but replace ‘visual representations’ with ‘worked examples’
● General argument for why the rule works (0-4 points) ○ 4pts - complete and correct general argument that a ‘new’ calculus student could
follow (i.e. narrate the argument as if you were teaching another student) ○ 3pts - nearly complete/correct general argument or lack of helpful narration ○ 2pts - complete/correct argument made for a particular function rather than in
general ○ 1pts - Any other attempt
● Quality of narration and exposition (0-4) ○ Is part 2 a cohesive piece of writing? ○ Are connections between representations and your general argument made explicit? ○ Are you attending to grammar, spelling, sentence structure? ○ Do you use clear and concise language? (Hint: avoid pronouns such as ‘it’, ‘the’,
‘that’)
○ Would a new calculus student be able to follow your argument?