Another Chalkdust Algebra (generic - Larson) question - about grading

[LNC]

I'm using the generic Larson text with Dana Mosely dvds aka "cheap Chalkdust". Maybe the real Chalkdust program has parent grading helps?

 

1. How do you weigh mid chapter quizzes, chapter tests, and review tests to calculate quarter, semester grade averages?

 

2. Do you count each problem equally in grading quizzes and tests?

[BibleBeltCatholicMom]

My husband (and uncle buck :glare:) teaches algebra but despite whatever he is "supposed" to be doing he checks everything and assigns redo work for missed problems but he only counts tests for her grade.

 

Oh, we paid for the whole shebang. We did get a paper discussing grading but we both knew that we were on the same page with grading so didn't worry about it. I do recall that the paper/dana/whatever states the obvious: parents ultimately decide on all that.

Edited September 26, 2012 by BibleBeltCatholicMom

[LNC]

I found this

http://www.chalkdust.com/testmeasure.html

 

I need to read through it carefully tonight. One problem I have is that if she makes one mistake in a long solution I count the entire problem wrong. The quizzes have about 26 problems so she gets a low B when she misses a few. Chalkdust recommends assigning a problem a value of 5 points total and each careless error within would be minus 1 point. He says grading math quizzes and tests is more of an art than a science. I'm still confused, and I think the idea is to be a bit subjective in grading. I can also weigh in homework with work shown correctly or even plan extra credit if I want. I like grading to be very objective, so this is difficult to get used to...

Edited September 26, 2012 by LNC

[nancy in nj]

We only used the Chapter tests for tests grades (80% of total grade) and counted homework for 20% based on effort/completion. She did the cumulative tests as review, and we counted this as homework.

 

We assigned a point value to each problem individually based on the number of significant steps and relative difficulty of the problem. The points per problem typically ranged from 2-6. If there was an error in step 3 of a 6 step problem and that error was carried forward but the methodology was correct throughout, we would only take 1 point off.

 

Nancy

[arstephia]

I grade the lesson/daily work and that makes up 50% of the grade. Tests and quizzes make up the other 50%. If my child bombs a homework assignment - a 59% or less they can rewatch the lesson and redo the lesson for full credit because they obviously didn't learn it the first time. This encourages them to take the daily work seriously and to pay attention to details. If I don't give daily work some credit, it shows in their test scores, probably because of the lack of attention to the process.

[kiana]

I found this

http://www.chalkdust.com/testmeasure.html

 

I need to read through it carefully tonight. One problem I have is that if she makes one mistake in a long solution I count the entire problem wrong. The quizzes have about 26 problems so she gets a low B when she misses a few. Chalkdust recommends assigning a problem a value of 5 points total and each careless error within would be minus 1 point. He says grading math quizzes and tests is more of an art than a science. I'm still confused, and I think the idea is to be a bit subjective in grading. I can also weigh in homework with work shown correctly or even plan extra credit if I want. I like grading to be very objective, so this is difficult to get used to...

 

It's not so much subjective, but rather that a single error shouldn't tank the whole problem.

 

Usually I mark (on longer exams) as -1 the first 2-3 times I see the same error and -2 after that. By the same error, I refer to types of errors such as improper factoring, distribution errors, sign errors, etc.

[BibleBeltCatholicMom]

It's not so much subjective, but rather that a single error shouldn't tank the whole problem.

 

Usually I mark (on longer exams) as -1 the first 2-3 times I see the same error and -2 after that. By the same error, I refer to types of errors such as improper factoring, distribution errors, sign errors, etc.

 

I agree . . . in part.

 

On homework, if my daughter makes a misstep but the problem is otherwise correctly worked (say, she added wrongly in a step but otherwise worked the steps themselves correctly) she has to find her own mistake, correct it, rewrite it. If she messed up the problem somehow, she has to correct the problem and gets a few more like it to solve until she gets them consistently right. In the begining I didn't understand why there were so many problems offered and why we did so few. Now I appreciate the well of problems when we need them. Having said that, the homework isn't graded per se. It is checked for mistakes and treated as above but no grade is recorded.

 

On the other hand, tests are different. If, on a test question, she works the problem correctly but misses something like above, she misses the question altogether; no partial credit. I feel that on tests, partial credit is a little too much mercy where not needed. She should scour her papers for mistakes and try hard not to make them.

 

This works for us. Now, I do not live in the world of high-stakes, real-life math but it doesn't seem like a place for partial credit. A digit off 5 steps back could mean the difference b/t lift off and not, between a sound structure and can't pass inspection, between the coolest roller coaster ever and . . . something else.

 

As I said, I don't live in that high stakes math world but my daughter is a pretty mathy kid and she might. For that reason (not to mention no partial credit on SATs, et c) I think the better approach for us is to teach her that she will make a few mistakes so she has to really scour her problems searching for her own mistakes and then correcting them before handing in. When she misses them in hmwk, she should be held accountable by redos and extras and when she misses them on tests she should miss them altoghther.

Edited September 27, 2012 by BibleBeltCatholicMom

[regentrude]

Chalkdust recommends assigning a problem a value of 5 points total and each careless error within would be minus 1 point. He says grading math quizzes and tests is more of an art than a science. I'm still confused, and I think the idea is to be a bit subjective in grading. I can also weigh in homework with work shown correctly or even plan extra credit if I want. I like grading to be very objective, so this is difficult to get used to...

 

A few thoughts:

1. I would definitely give partial credit for partially correct solutions - but grading this way requires the grader to have expertise and to be able to discern a simply arithmetic mistake from a basic conceptual mistake. Done this way, it is not really subjective. (College math exam will usually be graded this way.)

 

2. I do not believe in grading homework at all. Homework is a learning tool for acquiring mastery, and I would not want to punish a student for mistakes there. I would simply require incorrect problems to be corrected. "Extra credit" is equal to padding grades for things other than subject mastery.

 

3. I don't weight anything - I give a comprehensive final exam at the end of the semester. This way, I can test long term mastery and retention, the only thing that really matters in math. Knowing a concept only in the month it is introduced is worthless - knowing it after half a year is meaningful.

I would use chapter tests only as a diagnostic tool to determine if my student has mastered the material or if he needs to go back and review. I do not consider them a useful measure of long term mastery.

Edited September 27, 2012 by regentrude

[regentrude]

On the other hand, tests are different. If, on a test question, she works the problem correctly but misses something like above, she misses the question altogether; no partial credit. I feel that on tests, partial credit is a little too much mercy where not needed. She should scour her papers for mistakes and try hard not to make them.

 

Which may be almost impossible on harder material where a single problem takes two pages. In an ideal world, the student would not make any mistakes, but this ideal student does not exist.

If my student understands complex integration techniques, correctly identifies which technique to apply to the problem, carries out the calculation, and makes a minor arithmetic mistake that causes an incorrect final answer, this is not F performance - it is an A-. But it requires the grader to be able to understand and verify each step, to spot where the mistake happened, and to evaluate the importance of the mistake in the context of the complete problem.

[kiana]

Which may be almost impossible on harder material where a single problem takes two pages. In an ideal world, the student would not make any mistakes, but this ideal student does not exist.

If my student understands complex integration techniques, correctly identifies which technique to apply to the problem, carries out the calculation, and makes a minor arithmetic mistake that causes an incorrect final answer, this is not F performance - it is an A-. But it requires the grader to be able to understand and verify each step, to spot where the mistake happened, and to evaluate the importance of the mistake in the context of the complete problem.

 

Ayup.

[regentrude]

You know one thing I don't think we've talked about and what may be part of the problem is the complexity of the math. For example, I didn't give partial credit in Prealgebra and Alg I. Part of what they needed to be careful doing was to change negatives and other things like that.

 

However, in precalc and calculus are much more involved. So I think part of it may depend on the math.

 

No - it only depends on the level and complexity of the questions. I can make calculus tests that are just easy, simple computations following a specific pattern or problems grouped by technique to use - a way to make the same problems much, much easier to solve because it eliminates the thinking about the appropriate method.

In contrast, I can think of very complex algebra 1 problems I had on my kids' tests: word problems that require the student to correctly interpret the question, to determine which quantities to assign variables, to set up a system of multiple equations with multiple unknowns, and to solve the system. Easily 1-2 pages of work. A simple arithmetic mistake in this problem would be completely minor, if the student otherwise demonstrates mastery. (Of course, I can also create an algebra test that is purely mechancial and does not require actual thinking, just rote memorization of algorithms.)

[regentrude]

Well, I can tell you that Chalkdust does not have ANY problems that require 2 pages of work in Alg. I.. None.. I didn't have any that long either. Can you give me an example of a problem that complex?

 

Here is an example:

 

A box containing 3 oranges, 2 apples, and one banana weighs 15 units.

Another box containing 5 oranges, 7 apples, and 2 bananas weighs 44 units.

A third box containing 1 orange, 3 apples, and 5 bananas, weighs 26 units.

How much does eat fruit weight?

 

On DD's algebra 1 semester exam, she took full two pages to neatly write out the problem with all steps.

(ETA: We use AoPS, but I responded because consider the question of partial credit a fundamental one not limited to one particular curriculum.)

Edited September 27, 2012 by regentrude

[regentrude]

I googled just to make sure but that problem you gave is what is commonly taught in Alg II or College Algebra NOT Algebra I!!! Chalkdust has no problems like this.

 

But it is simply linear equations. :confused:

Systematically, systems of linear equations should be taught before quadratics, and quadratics should be included in any decent algebra 1 curriculum.

Our text covers systems (like the problem I quoted) in chapter 5; it is common consensus that the algebra 1 portion is through chapter 12 or 13.

So does your algebra 1 curriculum stop after linear equations with one variable???? No systems and no quadratics???

 

 

ETA: I just looked up the Chalkdust algebra 1 TOC:

http://www.chalkdust.com/algoneoutnew.html

Chapter 8:

Chapter 8- System of Linear Equations

 

 

8.1 Solving Systems of Equations by Graphing

8.2 Solving Systems of Equations by Substitution

8.3 Solving Systems of Equations of Linear Equations

8.4 Applications of Systems of Linear Equations

8.5 Systems of Linear Inequalities

 

So yes, it is covered.

Edited September 27, 2012 by regentrude

[kiana]

But it is simply linear equations. :confused:

Systematically, systems of linear equations should be taught before quadratics, and quadratics should be included in any decent algebra 1 curriculum.

Our text covers systems (like the problem I quoted) in chapter 5; it is common consensus that the algebra 1 portion is through chapter 12 or 13.

So does your algebra 1 curriculum stop after linear equations with one variable???? No systems and no quadratics???

 

 

ETA: I just looked up the Chalkdust algebra 1 TOC:

http://www.chalkdust.com/algoneoutnew.html

Chapter 8:

 

Chapter 8- System of Linear Equations

 

 

8.1 Solving Systems of Equations by Graphing

8.2 Solving Systems of Equations by Substitution

8.3 Solving Systems of Equations of Linear Equations

8.4 Applications of Systems of Linear Equations

8.5 Systems of Linear Inequalities

 

So yes, it is covered.

 

Found the chapter test for chalkdust's algebra 1 book as part of a preview on google books. Looks like they don't go beyond two variable systems.

 

This is not, btw, a slight on Chalkdust -- AOPS simply takes just about every topic further. Chalkdust is a very solid general course that will prepare a student amply for university.

[BibleBeltCatholicMom]

Here is an example:

 

A box containing 3 oranges, 2 apples, and one banana weighs 15 units.

Another box containing 5 oranges, 7 apples, and 2 bananas weighs 44 units.

A third box containing 1 orange, 3 apples, and 5 bananas, weighs 26 units.

How much does eat fruit weight?

 

On DD's algebra 1 semester exam, she took full two pages to neatly write out the problem with all steps.

(ETA: We use AoPS, but I responded because consider the question of partial credit a fundamental one not limited to one particular curriculum.)

 

My daughter had problems similar to that in 6th grade Singapore (IPs) but they tended not to take up two pages. Though we tend to have my daughter use grid paper for math so maybe that makes a difference. She had a private tutor at that time who liked to give partial credit but we discussed her out of that.

[LNC]

A few thoughts:

1. I would definitely give partial credit for partially correct solutions - but grading this way requires the grader to have expertise and to be able to discern a simply arithmetic mistake from a basic conceptual mistake. Done this way, it is not really subjective. (College math exam will usually be graded this way.)

 

2. I do not believe in grading homework at all. Homework is a learning tool for acquiring mastery, and I would not want to punish a student for mistakes there. I would simply require incorrect problems to be corrected. "Extra credit" is equal to padding grades for things other than subject mastery.

 

3. I don't weight anything - I give a comprehensive final exam at the end of the semester. This way, I can test long term mastery and retention, the only thing that really matters in math. Knowing a concept only in the month it is introduced is worthless - knowing it after half a year is meaningful.

I would use chapter tests only as a diagnostic tool to determine if my student has mastered the material or if he needs to go back and review. I do not consider them a useful measure of long term mastery.

 

This is very helpful - thanks... I will not "grade" homework, but I will insist on showing all steps - nothing done in her head. I think I will come up with a way to count mid chapter quizzes and homework as part of her grade - but the chapter tests will definately count for the vast majority. After reading the Chalkdust link I posted earlier I think I have a better idea on how to grade. I really benefitted from everyone's comments too...