Assigning grades in AOPS Intro to Algebra

[Kidlit]

My dd is in eighth grade and is working through AOPS Intro to Algebra. I am attempting to keep up with grades this year as practice for keeping a transcript in case she decides to homeschool highschool. We are using the review problems at the end of each chapter as a test of sorts. My question for AOPS users is how do you calculate the student's grade if they're good math students and engaged with the work but usually score about 50% correct the first time through the review problems? We're satisfied that AOPS is the best fit because she has tried other things, and AOPS is her thing. I usually grade her work and then she makes another pass at the problems she missed before we go over the ones she hasn't figured out. What feels right to me is crediting her back half of the points on the ones she figures out on her own after missing them once, but I'd love to hear other ideas.

 

 

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[regentrude]

I don't grade daily work. Daily work is for practice and learning, and I see no point in punishing a learner for working through hard problems. I give a comprehensive final exam at the end of the year, because long term retention and mastery are my goals in math. I have shared my exams on this board, search the archives.

[Kidlit]

I don't grade daily work. Daily work is for practice and learning, and I see no point in punishing a learner for working through hard problems. I give a comprehensive final exam at the end of the year, because long term retention and mastery are my goals in math. I have shared my exams on this board, search the archives.

I'm not grading daily work; these are the end-of-chapter problems.

Thanks for the exams!

 

 

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[domesticidyll]

For homework, it seems fine to me to grade on effort and completeness. And then weight the grade heavily toward the exam.

 

You could also assign one written proof, her choice of which challenge problem, per chapter, and grade those on quality of math and writing. AoPS has a page of hints on writing math proofs, and you can use the text as a model also.

 

The problems are meant to be hard enough that the student stumbles on a few--so grading on all the end-of-chapter problems feels a bit like penalizing the student for working at the appropriate level. 

[Kidlit]

You could also assign one written proof, her choice of which challenge problem, per chapter, and grade those on quality of math and writing. AoPS has a page of hints on writing math proofs, and you can use the text as a model also.

 

.

I really like this idea. Is this page of hints on the website? I don't remember seeing it in the book, though it is entirely possible that I missed it.

 

 

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[domesticidyll]

Here's the link to the first page:

 

https://artofproblemsolving.com/articles/how-to-write-solution

 

 

[domesticidyll]

This is a very short version that I've pieced together from the link above and from helpful grader comments:

 

Considering the problem

 

What exactly  am I being asked for?

What is tricky about this problem? (What do I need that I’m not given directly?)

What am I given? What can I do with what I am given? Have I used everything I’m given?

What strategies will be helpful in solving this problem?

 

Writing a discussion of the problem

 

Goal and strategy:

We are being asked for…

We will use a basic strategy of...

 

Setting up equations:

Name and define variables precisely.

When you set up an equation, explain what it represents or how you came up with it.

Embed math expressions and equations into a sentence.  (But don’t mix words into equations.)

 

Writing it out:

Give each equation its own line.

When you change an equation, be explicit about what change you made and what justified it.

Number different cases when using casework.

Use generous amounts of white space.

Use diagrams or drawings if helpful.

 

Helpful phrases:

We have / we are given…

Using the following justification, we do such-and-such to it…

Then we…

Now we have….

 

The answer:

Box your answer.

Give a brief justification of your answer.

For a proof, explain how we know it works for all cases.

Give your answer in sentence form in the same terms that the problem framed it in.

(This can be at the beginning or the end. Put it in its own paragraph.)

 

[Kidlit]

This is a very short version that I've pieced together from the link above and from helpful grader comments:

 

Considering the problem

 

What exactly am I being asked for?

What is tricky about this problem? (What do I need that I’m not given directly?)

What am I given? What can I do with what I am given? Have I used everything I’m given?

What strategies will be helpful in solving this problem?

 

Writing a discussion of the problem

 

Goal and strategy:

We are being asked for…

We will use a basic strategy of...

 

Setting up equations:

Name and define variables precisely.

When you set up an equation, explain what it represents or how you came up with it.

Embed math expressions and equations into a sentence. (But don’t mix words into equations.)

 

Writing it out:

Give each equation its own line.

When you change an equation, be explicit about what change you made and what justified it.

Number different cases when using casework.

Use generous amounts of white space.

Use diagrams or drawings if helpful.

 

Helpful phrases:

We have / we are given…

Using the following justification, we do such-and-such to it…

Then we…

Now we have….

 

The answer:

Box your answer.

Give a brief justification of your answer.

For a proof, explain how we know it works for all cases.

Give your answer in sentence form in the same terms that the problem framed it in.

(This can be at the beginning or the end. Put it in its own paragraph.)

 

Thank you!

 

 

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[regentrude]

I'm not grading daily work; these are the end-of-chapter problems.

 

I consider these daily practice as well. I would not expect my student to have mastered the material before working through those.

[Kidlit]

I consider these daily practice as well. I would not expect my student to have mastered the material before working through those.

I feel like we need some sort of in-the-middle checks to make sure she's mastering and retaining. Any ideas?

 

 

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[regentrude]

I feel like we need some sort of in-the-middle checks to make sure she's mastering and retaining. Any ideas?

 

In a homeschool, you get to see her work every day. You get to talk about math, see where she struggles, what questions she has. Those conversations should give you a good picture of her mastery and retention. Have her narrate a problem and explain the solution to you - that is the best way of seeing whether she understands.

[skimomma]

I have asked this question recently and have currently settled on a hybrid approach for Intro to Geometry.  Pre-high school, dd did Pre-A and Intro to Algebra with no formal grading.  Basically, she worked the problems, sometimes with help, until she understood each one and could move ahead.  This approach worked well for us so I wanted to keep the procedure the same but try to find a way to capture a "grade" for a transcript.

 

I grade all of the chapter exercises for completeness (is the problem statement well-represented in her work, is all work shown, etc...), effort, and neatness (can I follow what she is doing, can I read her writing, etc...?).  She works these problems until they are correct and understood so no grade attached that that.  Unless she does really sloppy work or makes no attempt at a problem, she gets 100%.  This is 30% of her "grade."  The review problems are assigned sort of like a test.  When those are complete, I grade them and she gets another stab at the ones she got incorrect.  75% back if she identifies and corrects the problem herself (these are almost always correct conceptually with a  simple math or copying error).  50% back if she needs a small directional "hint" after explaining to me the correct general direction.  25% back if I have to really walk her through the approach.  0% if I ultimately have to do the problem with her watching.  This is 40% of her "grade."  The final 30% are the midterm and final comprehensive exams.  

 

It sounds complicated but in reality is pretty simple.  I will adjust as necessary.  We are still pretty new to it.  I would rather not grade at all.  I don't think it does anything to help dd learn the material.  But for the sake of accountability, I feel I need to.

[Kidlit]

I have asked this question recently and have currently settled on a hybrid approach for Intro to Geometry. Pre-high school, dd did Pre-A and Intro to Algebra with no formal grading. Basically, she worked the problems, sometimes with help, until she understood each one and could move ahead. This approach worked well for us so I wanted to keep the procedure the same but try to find a way to capture a "grade" for a transcript.

 

I grade all of the chapter exercises for completeness (is the problem statement well-represented in her work, is all work shown, etc...), effort, and neatness (can I follow what she is doing, can I read her writing, etc...?). She works these problems until they are correct and understood so no grade attached that that. Unless she does really sloppy work or makes no attempt at a problem, she gets 100%. This is 30% of her "grade." The review problems are assigned sort of like a test. When those are complete, I grade them and she gets another stab at the ones she got incorrect. 75% back if she identifies and corrects the problem herself (these are almost always correct conceptually with a simple math or copying error). 50% back if she needs a small directional "hint" after explaining to me the correct general direction. 25% back if I have to really walk her through the approach. 0% if I ultimately have to do the problem with her watching. This is 40% of her "grade." The final 30% are the midterm and final comprehensive exams.

 

It sounds complicated but in reality is pretty simple. I will adjust as necessary. We are still pretty new to it. I would rather not grade at all. I don't think it does anything to help dd learn the material. But for the sake of accountability, I feel I need to.

Thank you for this! This is something like what I'm looking for. Dd likes grades, even though I don't. [emoji13] Also, that pesky transcript seems to require it, at least in my mind.

 

 

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[daijobu]

I copy (by hand) my old fading purple mimeographed high school exams.  Especially in the Intermediate level AoPS books it gives my kids a better understanding of what expectations are for a regular high school class (i.e., no Putnam problems).  

 

I also like to see improvements in their AMC scores, but sometimes the difficulty varies year to year so not always reliable.  

[Kidlit]

I copy (by hand) my old fading purple mimeographed high school exams. Especially in the Intermediate level AoPS books it gives my kids a better understanding of what expectations are for a regular high school class (i.e., no Putnam problems).

 

I also like to see improvements in their AMC scores, but sometimes the difficulty varies year to year so not always reliable.

I like the idea of giving the student a “regular†math test. Thanks!

 

 

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