Saxon Record Keeping

[Psittacula]

Hi,

 

We are using Saxon as our high school math curriculum, and it is going well. However, I do not know how to keep records for this. My student looks at the problem sets and works them out on scratch paper, although she skips many steps sometimes because she is good at mental math. After that, she checks her work, and corrects whatever she got wrong. For the tests however, we are not sure if she should use this scratch paper approach (look at questions, solve on scratch paper, write final answer) or if she should copy all of the test questions on a separate paper and show all of her work. She prefers not to do this because she can work out many of the steps in her head.

 

For the tests, this is what we have been doing so far:

1. Write the question numbers (not the questions themselves) on a piece of paper
2. Solve each question on another piece of paper (scratch paper)
3. Write final answers beside their question numbers on the first piece of paper

Does anyone happen to have some completed problem sets and tests that we could look at? I want to make sure I keep good math records, as she is interested in a STEM career (veterinarian).

 

Thank you all in advance.

[regentrude]

We are not using Saxon, but I want to chime in, since the question is not Saxon specific:

 

Writing out a complete solution to a math problem is absolutely essential. She needs to learn this and show all her work (except, of course, simple arithmetic steps she can do in her head).

How are you going to grade a test if the final answer is incorrect? You need to be able to evaluate her entire process.

Problems will get longer and more complex, and the final answer is only a tiny piece of the entire puzzle.

 

ETA: The problem should be stated, and the solution should be written in such a way that another person can understand what she does in each step. One equation per line. Equal signs aligned underneath each other. No run-on equal signs between expressions that are not, in fact, equal. Final answer boxed or underlined.

And if you are concerned about record keeping, it would be doubly important to have a record of her actual work, and not simply an answer sheet.

 

In college, the final answer may be 5% of the grade - the remaining 95% are for correct procedure.

[Twigs]

We are not using Saxon, but I want to chime in, since the question is not Saxon specific:

 

Writing out a complete solution to a math problem is absolutely essential. She needs to learn this and show all her work (except, of course, simple arithmetic steps she can do in her head).

How are you going to grade a test if the final answer is incorrect? You need to be able to evaluate her entire process.

Problems will get longer and more complex, and the final answer is only a tiny piece of the entire puzzle.

 

ETA: The problem should be stated, and the solution should be written in such a way that another person can understand what she does in each step. One equation per line. Equal signs aligned underneath each other. No run-on equal signs between expressions that are not, in fact, equal. Final answer boxed or underlined.

And if you are concerned about record keeping, it would be doubly important to have a record of her actual work, and not simply an answer sheet.

 

In college, the final answer may be 5% of the grade - the remaining 95% are for correct procedure.

:iagree:  :iagree:  :iagree:

 

I am a chemistry tutor and many of my students will bring me a problem with an incorrect answer. (Computer generated and graded problems.) They will have little to nothing written down and expect me to help them, which I cannot do. I make them write down the steps. Your student needs to be learning not only math, but how to communicate their logic process to others. In a STEM field, this is critical. 

 

Also, when she gets into chemistry and physics, she should be using unit analysis in every problem that requires calculation. Several of my students routinely miss questions because they are only doing the math calculations and not catching when the units don't cancel.

 

Best wishes.

[Psittacula]

Thank you both for your replies, I will make sure she starts showing her work. Do you think getting the solutions manuals will help her to format her answers properly? We are doing fine so far with only the answer booklet, but I am thinking about the future books where she may need the solutions manual. Also, should she be writing the questions themselves on a separate piece of paper, and then work out the solutions on the same paper?

 

Sorry to bother you two, but do you happen to have some sample work that we could look at? I would like to know how she should format her answers.

 

Also, this is kind of off-topic, but we are using Apologia as well, and I am not sure how she should format her answers for the tests. So far, we have been using the same approach we used with Saxon. She would read the questions, and put the question number plus her answer on a different sheet of paper. Should she be copying the questions themselves as well? I am sorry if this seems so basic, but this is our first time homeschooling high school.

[AmyontheFarm]

I tell my kid, "When in doubt, write it out"

 

I would get her into the habit of writing every step out in science, math, etc.

[regentrude]

Thank you both for your replies, I will make sure she starts showing her work. Do you think getting the solutions manuals will help her to format her answers properly? We are doing fine so far with only the answer booklet, but I am thinking about the future books where she may need the solutions manual. Also, should she be writing the questions themselves on a separate piece of paper, and then work out the solutions on the same paper?

 

Sorry to bother you two, but do you happen to have some sample work that we could look at? I would like to know how she should format her answers.

 

Also, this is kind of off-topic, but we are using Apologia as well, and I am not sure how she should format her answers for the tests. So far, we have been using the same approach we used with Saxon. She would read the questions, and put the question number plus her answer on a different sheet of paper. Should she be copying the questions themselves as well? I am sorry if this seems so basic, but this is our first time homeschooling high school.

 

Unless the solutions manual is outstanding, it will not contain a properly written out solution showing all the steps - and especially not written the way the student should (i.e. single equation per line)

 

She should begin by writing the problem if it is a purely mathematical problem like an equation to solve. If it is a long word problem, no need to copy the complete problem, but she should list what is given and what she is looking for, and she should assign all variables in a way another person can understand. (So, if it's a problem about a number of apples and a number of pears, she should define: a=# apples, p=# pears before using the symbols when she sets up the corresponding equation.

 

Doesn't your textbook have worked out examples???

 

How did you have her write out math before high school? It's not that something magically changes in high school and there are new requirements for writing math properly - anything she learned about writing proper complete solutions in prealgebra should still apply, there's now only more of it.

 

ETA: For WHAT are you using Apologia? Science? The problem should be stated, if appropriate with a sketch defining all variables she uses, and the complete calculation from starting equation to final answer should be below. It needs to be self contained .

[SparklyUnicorn]

Either the solutions manual or the Teacher CD set will help you with this.  I prefer the Teacher CD.  It is a bit more thorough and someone talks it out on top of writing down the steps. 

 

The solutions manual sometimes leaves out steps I think would ideally be shown, but it does show steps. 

 

[RegularMom]

We use Saxon, and will continue for high school, and yes, we show all work. I have them start by copying the original problem onto their paper and then showing each step on subsequent lines. We go through a lot of paper each year, yes, but it's important to keep the steps organized.

 

I tell them it's in their best interest to show their work, because that way, I can award partial credit for answers that are only off by a small calculation error. 

[Teachin'Mine]

Which level is she doing?  We found the solutions manual very helpful.  When a concept is first introduced, all the steps are written.  As the problems get more complex, some of the more basic steps aren't shown in the solution.   It depends on the student, but for most I wouldn't recommend that they do their own checking.  IMO a lot more is learned by looking at the steps done on their own paper, or re-doing the problem if it wasn't written out sufficiently, and finding and correcting their mistakes.  Many students would just take the short cut and look at the solution and be done with it.  Looking at an answer key alone is even worse.  Math builds quickly in the high school texts and any concepts missed will lead to problems later. 

[Sebastian (a lady)]

I'll share a painful lesson learned. Even though my son had been told for years to show his work, when he took his first dual enrolled CC math class on the first in class test the instructor said they didn't need scratch paper, but could use the back of the test papers for calculations. Ds took to mean he didn't need to show his work. He got a low C on the test on which he'd only put his final answers.

He took the test and reworked every problem. Then he met with the instr. in many cases there was a small math error carried forward. Had he shown his work he would have had a low A on the exam. He spent the rest of the semester recovering the grade he'd tossed away by not showing work.

 

In my opinion it's just as important to show work on the problems you don't understand well. This gives the grader insight into where the student is struggling.

[Psittacula]

Thank you all for your input. Yes, I will make sure she starts showing her work. Should this be done for both the problem sets and the tests? I am asking this because the problem sets are rather lengthy and I only use the tests for grading purposes. Since there are so many tests, I figured that I might as well only keep those for my records. I am wondering if she should only show her work for the tests because it would seem like a waste of time if she worked out all of the solutions for the problem sets when they are going to be recycled anyway. If she should show her work for the problem sets, would it be a good idea if she only worked out the even or odd problems?

[MysteryJen]

My (unpopular in this house) opinion is that you need to show all your work for all problem sets and all tests.

[regentrude]

Thank you all for your input. Yes, I will make sure she starts showing her work. Should this be done for both the problem sets and the tests? I am asking this because the problem sets are rather lengthy and I only use the tests for grading purposes. Since there are so many tests, I figured that I might as well only keep those for my records. I am wondering if she should only show her work for the tests because it would seem like a waste of time if she worked out all of the solutions for the problem sets when they are going to be recycled anyway. If she should show her work for the problem sets, would it be a good idea if she only worked out the even or odd problems?

 

She needs to learn to show her work on EVERY problem. It needs to become second nature to write the problem out correctly.

Expecting this on tests only will not teach her this very important skill.

 

Why would you consider writing solutions a "waste of time"? You don't write the solutions for some record, you write the solutions to learn how to document math problems. Because with any decent math program, problems will soon be so complex that they cannot be solved without writing down many, many steps.

 

She will need the very same skills in science.

[MarkT]

Thank you all for your input. Yes, I will make sure she starts showing her work. Should this be done for both the problem sets and the tests? I am asking this because the problem sets are rather lengthy and I only use the tests for grading purposes. Since there are so many tests, I figured that I might as well only keep those for my records. I am wondering if she should only show her work for the tests because it would seem like a waste of time if she worked out all of the solutions for the problem sets when they are going to be recycled anyway. If she should show her work for the problem sets, would it be a good idea if she only worked out the even or odd problems?

For the problem sets the problem number and the next step of the solution should suffice. Also no units (sq inches, etc) then no credit!

[Twigs]

Here's an example. Hope it helps.

 

Make Your Homeschooler Show Work

 

[regentrude]

Here's an example. Hope it helps.

 

Make Your Homeschooler Show Work

 

The real problem with the second example is not that too few steps are written, but that there is a mistake using the distributive property when multiplying 2(x+5). If a student got the correct answer despite this mistake, it would suggest that the student consulted unapproved aids, like the solution manual.

 

The examples show how a beginning algebra student should document her work.

Showing just the amount of "too few" in the 2nd example (without the mistake, of course) would be entirely appropriate for an advanced algebra student who does not need to write all the operations explicitly.

[SparklyUnicorn]

Here's an example. Hope it helps.

 

Make Your Homeschooler Show Work

 

Yeah and unfortunately the solutions manual does skip a lot of steps I'd show.  If they add or subtract or anything like that, they don't show that.  They just show the result.  So when I look at it I have to first figure out what they did.  In the simple examples that's not a big deal, but the problems aren't usually that simple.

 

That's why I like the Teacher videos better.  They show all the steps and talk it out.  It's just not as quick to pull up the answers.  With A 1 I had the teacher discs.  Now with A 2 I decided to try the solutions manual.  I think next book I'll get both. 

[Twigs]

Regentrude and SparklyUnicorn,

 

Thanks for commenting on that link. I couldn't find anything better. I hope I can do a problem myself and upload it for an example of what I prefer to see.

 

 

The real problem with the second example is not that too few steps are written, but that there is a mistake using the distributive property when multiplying 2(x+5). …

  :eek:  I found that at work last night. I did notice something wrong with that example, but could not spend enough time to figure it out! Thanks 

[Psittacula]

Here's an example. Hope it helps.

 

Make Your Homeschooler Show Work

 

Thank you so much for that link, it is very helpful and gives us an idea of how her work should look like. When it comes to showing her work, what basic steps can she skip? I remember regentrude mentioned that you do not need to list certain steps.

[regentrude]

Thank you so much for that link, it is very helpful and gives us an idea of how her work should look like. When it comes to showing her work, what basic steps can she skip? I remember regentrude mentioned that you do not need to list certain steps.

 

A learner should show everything. I strongly encourage you to make her show explicitly which operation she performs in each step.

The example in the link does this below equation; back home, we were taught to draw a vertical line behind the equation and list after that the operation we were going to perform on both sides to obtain the next step.

 

Now, a student proficient in algebra would no longer be required to show the operation explicitly, but should still show the new equation resulting from the operation performed on both sides.

[Psittacula]

Thanks regentrude. Does this mean that if she needs to, for example, add 1 to both sides of the equation, she does not have to write it out underneath? All she has to do is write the result of the adding underneath? I remember that you said the second example on the site would be fine if the distributive property was used correctly.

[regentrude]

Thanks regentrude. Does this mean that if she needs to, for example, add 1 to both sides of the equation, she does not have to write it out underneath? All she has to do is write the result of the adding underneath? I remember that you said the second example on the site would be fine if the distributive property was used correctly.

 

It depends on the student's level of mastery.

If I had a student just begin to learn how to manipulate equations in algebra 1, I would require the student to write the +1 explicitly and then the next equation.

For a student who is half way through algebra 1 and proficient in manipulating equations, I would no longer require this step.

For a student who is in precalculus and for whom these algebraic manipulations have become second nature, I would be fine if the student did multiple operations in a single step. There will be other things that need to be shown.

 

 

[regentrude]

To take the second example: 2(x+5)=- 3x- 6

 

I would require a beginning student to write:

2x+10=- 3x- 6     |+3x    i.e. list operation to be performed, and do one step at a time

5x+10=-6            |-10

5x      =-16          |:5

x        =-16/5

 

but I would expect an advanced student to write:

2x+10 =- 3x- 6       i.e. omit explicit stating of operation and allow multiple steps simultaneously

5x      =- 16

x        = - 16/5

 

The explicit listing of every single operation is a learning tool. It visualizes for the learner what is going on and reminds her to perform the operation on both sides.

The second way to write the problem still documents all the work, since anybody can see what the student did.

An advanced student will no longer think of it as "we add 3x to both sides so the -3x goes away on the right". The advanced student will think of it as  "we are moving the -3x to the left side" - and once this way of thinking about it is achieved, showing the explicit operation is no longer necessary, because that step is a learning tool and not necessary for documenting the problem.

 

 

[kiana]

I would find the second example entirely appropriate for someone who was not a beginning algebra student. I think that there's such a thing as writing out too much -- it wastes time and space and obfuscates the flow of the problem -- although I would never mark off points for writing out too much.

 

Now, I do write out my examples like the first example even in precalculus or calculus, but that is because many of my students have inadequate algebra backgrounds for the level of course they are taking and cannot follow their own notes if I do not write that out. 

 

I actually just had a discussion with someone last week about not writing down steps where the student insisted that it was ok to do a specific step in the head. Well, since it was something that had been wrong on three week's worth of homework ... no, it's not ok. 

[Psittacula]

Thank you so much regentrude! You have been very helpful. I will make sure she starts documenting her work properly and I will be sure to show her your examples. For that vertical line method, I can see that ":" means division, but what is the symbol for multiplication?

 

Thanks again everyone for all your help.

[kiana]

: is just European notation for division. You can write whatever makes sense to you -- for a student who has received their math education in America using a standard division symbol is probably going to make more sense. The important thing is that you clearly indicate which operation you are performing. 

[regentrude]

Thank you so much regentrude! You have been very helpful. I will make sure she starts documenting her work properly and I will be sure to show her your examples. For that vertical line method, I can see that ":" means division, but what is the symbol for multiplication?

 

Thanks again everyone for all your help.

 

: is European for division. You would probably want to use a slash, or a slash with dots.

The symbol for multiplication would be a dot or a star.

 

Just to add one interesting tidbit:

In Germany, we denote division by a colon: and multiplication by a dot. The rule for order of operations children are taught in school is "dot operations before line operations". Dot operations are : and ., while line operations are + and -.

This grouping of operations removes the flaw of the US mnemonic PEMDAS which seems to suggest a hierarchy between multiplication/division and addition/subtraction.

[Sebastian (a lady)]

For the problem sets the problem number and the next step of the solution should suffice. Also no units (sq inches, etc) then no credit!

I encourage my kids to copy the problem if it's written in the assignment.

 

This reduces errors made when they are computing the first step in their head as they move from book to paper. It's harder to drop a term or a negative sign if it's right there on the line above.

 

Also I've found that the act of recopying the problem often gets them part of the way through solving it. Something in the copying act helps them see their way through.

[Sebastian (a lady)]

On the question of skipping problems in Saxon, I would recommend against it. The spiral progression is based in part on the fact that a student will be reviewing concepts withing the mixed practice sets. If you skip half you may skip important review. The problems are also sometimes increasing in difficulty such that a new concept has been hinted at within the preceding practice.

[SparklyUnicorn]

I encourage my kids to copy the problem if it's written in the assignment.

 

This reduces errors made when they are computing the first step in their head as they move from book to paper. It's harder to drop a term or a negative sign if it's right there on the line above.

 

Also I've found that the act of recopying the problem often gets them part of the way through solving it. Something in the copying act helps them see their way through.

 

The way I've shown my son how to solve the problems step by step basically requires the problem to be copied.  I work the steps under the problem starting with the original problem.  That's how I was taught.  

[MarkT]

The real problem with the second example is not that too few steps are written, but that there is a mistake using the distributive property when multiplying 2(x+5). If a student got the correct answer despite this mistake, it would suggest that the student consulted unapproved aids, like the solution manual.

 

The examples show how a beginning algebra student should document her work.

Showing just the amount of "too few" in the 2nd example (without the mistake, of course) would be entirely appropriate for an advanced algebra student who does not need to write all the operations explicitly.

   

This is how I was taught back in the day - note we kept the equation in balance and it is easier to transition to the "later on method"

   (now they teach the Example 2 "good work" method which I don't like)

 

beginning method

    2(x+5)   = -3x-6

    2x+10    = -3x-6

 3x+2x+10    = -3x-6+3x

    5x+10-10 = -6-10

        5x   = -16

         x   = -16/5

 

   later on method

     2(x+5) = -3x-6

     2x+10  = -3x-6

       5x   = -16

        x   = -16/5

[SparklyUnicorn]

The first method is more familiar to me.  Except I'd write some of that vertically.