Grading Algebra 1

[Jkacz]

Hi everyone.  DS is in 8th grade and has started Algebra 1 using Foerster and Math without borders.   This is the first time I’m having to grade and I’m unsure how to weight everything (homework, quizzes, final exam, etc).  DS has diagnosed anxiety and sometimes struggles with testing, so I’d prefer to weight exams as low as possible but I’m not sure what’s reasonable.  Any advice?

Jenn

[NewIma]

We are doing the exact same programs and I am also unsure about this. Thanks for asking the question!

[8filltheheart]

I dont grade like a traditional classroom teacher bc we dont homeschool like a traditional classroom. I teach to mastery, so we dont progress until they have the equivalent of a high A understanding. For example, right now my 9th grader is taking physics. She probably has a low B level understanding at the end of a chpt. When we finish a chpt, we go back to the beginning and repeat the chpt. Starting the chpt over means she has the bigger picture already and reworking everything makes all those sort-ofs  become lightbulb moments and all the connections are being made.  She is producing solidly A level work by the end. (We are 10 wks into our yr.)

That level of understanding is my objective. Not a this assignment is worth X %. In our school profile and course descriptions I state we teach to mastery. By 12th grade they have mastered their own studying skills and know how to go back and study to mastery independently. They are successful college students, so it is an approach that works here.

Edited September 23, 2020 by 8FillTheHeart
Wrong # of wks completed

[mom31257]

This is how I weight all high school grades. 

Daily work, participation in discussions or activities  1/6 of grade

Quizzes, small assignments, shorter essay responses  1/3 of grade

Tests, longer writing assignments, bigger projects     1/2 of grade 

When I am grading math, I give partial credit if they show all their work and a full understanding of the processes but make a careless mistake. It encourages them to show all the steps when some are prone to skip a lot and just do them in their head. 

 

 

 

[EKS]

For math I do 25% homework and 75% assessments.  I try to keep the semester exams at around 10-15% of the grade.  Inside the assessment category, I use the point value to weight assignments--so a quiz might be 10 points, a test 100 points, and a semester exam 200 points.

I teach to mastery, so homework is always corrected to 100% (and recorded as 100%), and I don't give tests until I'm sure that the student is capable of getting an A.  Note that with 93% average on tests (the top of the A minus range), the 25% for homework only increases the grade by 1.75% (to 94.75%).  ETA:  Don't tell the student this--I like them to think that the homework piece is key to getting a good grade.  And it is in the sense that they can't get above a 75% without it.  But none of my students has ever figured out on their own that when they are getting an A average on the tests, the percent of their grade contributed by the homework is negligible. 

I also make sure that the grade the student gets is in line with what I know to be true about their achievement in the class.  Because of this, I don't take off points for lateness or anything else unrelated to their demonstrated knowledge of the material.  

I came up with this weighting scheme many years ago after looking through the schemes of the math teachers at the local public high school.  They all seemed to have about 25% of the points derive from things like homework completion, notebook checks, and attendance and 10-15% from the semester exams. 

Edited September 23, 2020 by EKS

[regentrude]

1 hour ago, 8FillTheHeart said:

I dont grade like a traditional classroom teacher bc we dont homeschool like a traditional classroom. I teach to mastery, so we dont progress until they have the equivalent of a high A understanding. For example, right now my 9th grader is taking physics. She probably has a low B level understanding at the end of a chpt. When we finish a chpt, we go back to the beginning and repeat the chpt. Starting the chpt over means she has the bigger picture already and reworking everything makes all those sort-ofs  become lightbulb moments and all the connections are being made.  She is producing solidly A level work by the end. (We are 12 wks into our yr.)

That level of understanding is my objective. Not a this assignment is worth X %. In our school profile and course descriptions I state we teach to mastery. By 12th grade they have mastered there own studying skills and know how to go back and study to mastery independently. They are successful college students, so it is an approach that works here.

This. There is no value in progressing to the next topic in math until the previous topic has been thoroughly mastered.
There are different ways to achieve this.

As a homeschooler, I was able to see my kids' understanding on a daily basis as they worked through the problems. I see no point in giving low grades for daily work, since that is practice, and punishing a learner for mistakes does not accomplish anything. A wrong problem is redone, not just until the answer is correct, but until the student understands the reason behind every step. 
We only tested at the end of the semester when they had to demonstrate cumulative mastery. If that isn't there, they went back to review until they had it. 
Testing math in bite sized portions and not aiming for cumulative long term retention and mastery is the root of many of the issues I see in my college students. You don't have to make it into "high stakes" tests, or call it "test" at all - but advancing a student who has not mastered and retained the material from the entire course is doing the student a grave disservice.

Edited September 23, 2020 by regentrude

[Ausmumof3]

1 hour ago, 8FillTheHeart said:

I dont grade like a traditional classroom teacher bc we dont homeschool like a traditional classroom. I teach to mastery, so we dont progress until they have the equivalent of a high A understanding. For example, right now my 9th grader is taking physics. She probably has a low B level understanding at the end of a chpt. When we finish a chpt, we go back to the beginning and repeat the chpt. Starting the chpt over means she has the bigger picture already and reworking everything makes all those sort-ofs  become lightbulb moments and all the connections are being made.  She is producing solidly A level work by the end. (We are 12 wks into our yr.)

That level of understanding is my objective. Not a this assignment is worth X %. In our school profile and course descriptions I state we teach to mastery. By 12th grade they have mastered there own studying skills and know how to go back and study to mastery independently. They are successful college students, so it is an approach that works here.

I love this in theory but how do you get your kids buy in with this?  Mine get bored and just want to be done.

[8filltheheart]

16 minutes ago, Ausmumof3 said:

I love this in theory but how do you get your kids buy in with this?  Mine get bored and just want to be done.

I'm not sure how to answer bc we have never approached school as something that is checked off a list as done and move on. They aren't reading a text, doing worksheets, taking a test, check off, and move on to the next thing that needs to be checked off a to-do list to graduate. My kids are actively involved in what they study and what they use for their courses. They know the onus is on them to succeed for their own goals and that no one can do that for them.  They are also raised to see learning as their vocation in childhood and that that is how they honor the gifts bestowed on them by God. 

It is hard to encapsulate in a paragraph bc our homeschool is not just school at home. It is a lifestyle and a parenting philosophy.

[mom31257]

While I think it is very important in math to master skills before moving on and homeschooling gives us that flexibility, I feel that doing that for all of school and never letting them experience a lower grade in a subject won't prepare them for real life. They will not get to keep doing things over and over until they get them right on jobs or in college classes. 

[8filltheheart]

1 minute ago, mom31257 said:

While I think it is very important in math to master skills before moving on and homeschooling gives us that flexibility, I feel that doing that for all of school and never letting them experience a lower grade in a subject won't prepare them for real life. They will not get to keep doing things over and over until they get them right on jobs or in college classes. 

That is not our experience at all.  I have 6 adult kids who were all homeschooled through to graduation. 3 of those are college grads who graduated with honors, a 4th a college sr with a 4.0.  Of the older 3, 1 is a chemE, dad of 4 with a SAHW, and a great career. Another is a mom of 2 also with a great career. The other is a 3rd yr grad student at Berkeley. Another of our adult kids is autistic who has a full-time job and is an incredibly hard worker.  Very proud of his accomplishments. Our 6th is a college freshman who currently has all As in her classes. 

Modern educational grading paradigms don't dictate the sole path to success.

[8filltheheart]

7 minutes ago, Æthelthryth the Stormy said:

I disagree. It teaches them to better communicate where and when they are struggling. You are right that you don’t always get second chances in the workplace, but you are more likely to be given grace if you can ask questions and admit you don’t have to full picture and/or could use assistance than just doing a poor job and not caring that it wasn’t the best you could do. 

All I could think of when I read this is how ds's workplace quickly learned not to expect him to take group minutes or stand up and write brainstorming responses if they wanted other people to be able to read the words. His workplace doesn't care he can't spell without spell check bc he is a great engineer. 🙂 They are wise enough to recognize his strengths and ignore weaknesses that don't matter for his actual job performance. Yes, employers do do that. 

[EKS]

1 hour ago, Ausmumof3 said:

I love this in theory but how do you get your kids buy in with this?  Mine get bored and just want to be done.

Easy--you structure your homeschool so that they can't be "done" until the understanding (and fluency) is at mastery.   

That said, I have them take tests in math because I think that test taking is an important skill.

[8filltheheart]

3 minutes ago, mms said:

I see the homeschool mastery approach as setting a higher standard and expectations and learning that it is not the grade that matters but the knowledge.

This. Exactly. Understanding is paramount. Work on it until you understand. FWIW, my kids go to college and know how to do this. They have peers who expect teachers to tell them exactly what they need to know for tests and that is all they care about. The mindset is very different.

[mom31257]

I understand the philosophy behind working to understanding. And I do want my kids to learn from their mistakes, but you can learn those lessons without redoing grades until they are all As.

I have only graduated one who is out in adult life, and she graduated college as a nurse with a very high GPA, kept her full tuition scholarship the entire time, and is doing well on her job. So I guess taking the approach I did hasn't really hurt her. 

Every family has their own philosophies in homeschooling, which is what I think the OP wanted to hear. And I don't think doing a more school at home approach is terrible. I had a wonderful school experience growing up. I learned so much from really great teachers. From what I read on here, many had poor teachers in their schools and didn't learn all they could. I think my experience might be the exception to the rule, but it has shaped how I wanted to approach school with my own kids. 

[mom31257]

52 minutes ago, Æthelthryth the Stormy said:

I disagree. It teaches them to better communicate where and when they are struggling. You are right that you don’t always get second chances in the workplace, but you are more likely to be given grace if you can ask questions and admit you don’t have to full picture and/or could use assistance than just doing a poor job and not caring that it wasn’t the best you could do. 

My point is about getting grades to As and never giving lower than that. I don't think a B instead of an A always means they didn't care or do the best they could do. For some kids, a B in a particular subject might be the best they can do. For example below, her son is not a good speller. So that is something he didn't really master. We all have weaknesses and areas that will be more of a struggle than others. 

 

39 minutes ago, 8FillTheHeart said:

All I could think of when I read this is how ds's workplace quickly learned not to expect him to take group minutes or stand up and write brainstorming responses if they wanted other people to be able to read the words. His workplace doesn't care he can't spell without spell check bc he is a great engineer. 🙂 They are wise enough to recognize his strengths and ignore weaknesses that don't matter for his actual job performance. Yes, employers do do that. 

 

[Jkacz]

OP here - I think this is why I’m struggling. My boys have used Math Mammoth through grade 7. We would work through a chapter and when we thought they mastered the material, they would take the chapter quiz as a way to verify that there were no gaps. Anything they missed, we would redo.  There were no grades, we would just go over anything until they were completely fluent in it.  
 

Now I’m trying to figure out how to translate this to a “transcript”.  And with a child with anxiety, the idea of quizzes and tests being “high stakes” rather than an assessment tool is a problem.  As an example, chapter 1 in Foerester is all review for him but he really struggled mentally taking the test (he ended up with 96%) because of a few boneheaded mistakes. He can do his math daily work in minutes joking how easy it is, but because it was a test, it took him hours.  
 

We’re going to continue to teach to mastery - I don’t know how you can’t in math, but how do I approach giving him a grade?

[Lilaclady]

I don’t think the pp’s meant redoing a grade until the student has an A. Students don’t always have to make an A in every subject. With math, my students do the exercises and grade them by themselves. Then if they miss any, we go over it and see if it was just a simple mistake or more a comprehension issue. Because I don’t stress the mistakes, they have learnt that when they don’t understand, we go over it again. I do the same with science. History and Lang arts are a bit different to do that way but teaching to mastery really do produce better results. 

[mom31257]

9 minutes ago, Jkacz said:

OP here - I think this is why I’m struggling. My boys have used Math Mammoth through grade 7. We would work through a chapter and when we thought they mastered the material, they would take the chapter quiz as a way to verify that there were no gaps. Anything they missed, we would redo.  There were no grades, we would just go over anything until they were completely fluent in it.  
 

Now I’m trying to figure out how to translate this to a “transcript”.  And with a child with anxiety, the idea of quizzes and tests being “high stakes” rather than an assessment tool is a problem.  As an example, chapter 1 in Foerester is all review for him but he really struggled mentally taking the test (he ended up with 96%) because of a few boneheaded mistakes. He can do his math daily work in minutes joking how easy it is, but because it was a test, it took him hours.  
 

We’re going to continue to teach to mastery - I don’t know how you can’t in math, but how do I approach giving him a grade?

Is it possible for you to give him an assignment that is review of the material and not tell him you are grading it as a test grade? Then I would grade it to see how he does without the idea of it being a test. 

[Jkacz]

I think this is the heart of why I’m struggling. DH is a doctor. He struggled getting into medical school because he wasn’t a great test taker.  Don’t get me wrong, he had good grades and MCAT scores, but they weren’t the highest.  But after college and med school, he’s excelled.  He’s now a very highly thought of specialist, chair of his department, and on the Medical Executive Committee of the hospital.  His patients love him and other doctors seek him out for advice. 
 

DS takes after his father. It’s not that he doesn’t know the material, he does.  He’s great at math. The problem is how do I reflect that on a transcript?

 

[Not_a_Number]

I think I'd probably do "homework" to mastery but perhaps graded tests to get them used to timed situations. That being said, this is entirely theoretical since my oldest kid is 8. 

[EKS]

1 minute ago, Jkacz said:

I think this is the heart of why I’m struggling. DH is a doctor. He struggled getting into medical school because he wasn’t a great test taker.  Don’t get me wrong, he had good grades and MCAT scores, but they weren’t the highest.  But after college and med school, he’s excelled.  He’s now a very highly thought of specialist, chair of his department, and on the Medical Executive Committee of the hospital.  His patients love him and other doctors seek him out for advice. 
 

DS takes after his father. It’s not that he doesn’t know the material, he does.  He’s great at math. The problem is how do I reflect that on a transcript?

I'd use this opportunity to actively work with him on how to take tests.

[regentrude]

33 minutes ago, mom31257 said:

My point is about getting grades to As and never giving lower than that. I don't think a B instead of an A always means they didn't care or do the best they could do. For some kids, a B in a particular subject might be the best they can do. For example below, her son is not a good speller. So that is something he didn't really master. We all have weaknesses and areas that will be more of a struggle than others. 

I agree, but I see math as fundamentally different. There really is no point in advancing a  student who does not understand the concept thoroughly, because that will mean they won't be able to understand any concept that builds on this, and the difficulties will compound.
Very different from spelling . You can be a rotten speller and still read literature, and you can know nothing about Charlemagne and still learn about the French revolution - but a kid who cannot add fractions will carry this struggle through algebra, geometry, trig, calculus, physics, chem etc. Chalking that up as a "weakness" and moving on is a great disservice.

[regentrude]

33 minutes ago, Jkacz said:

OP here - I think this is why I’m struggling. My boys have used Math Mammoth through grade 7. We would work through a chapter and when we thought they mastered the material, they would take the chapter quiz as a way to verify that there were no gaps. Anything they missed, we would redo.  There were no grades, we would just go over anything until they were completely fluent in it.  
 

Now I’m trying to figure out how to translate this to a “transcript”.  ..

We’re going to continue to teach to mastery - I don’t know how you can’t in math, but how do I approach giving him a grade?

Easy. If mastery has been achieved - however you define and measure mastery - that's an A. 

There is no reason for complicated weighted formulas with daily work and homework and quizzes and tests (and colleges don't care to see such a formula from you), because in a homeschool, you have other ways of ascertaining that your kid has understood and mastered the material. You could simply have a conversation, aka an oral exam, in the tradition of the European universities 🙂

Edited September 23, 2020 by regentrude

[cintinative]

I'm hoping this isn't off-topic, but one reason that various prior posters keep pushing mastery is that it is SO very important with math.  Algebra I lays a foundation for all the later math that your student will take. So what I have seen on here so many times is--let it take however long it takes for them to understand the material and master it. Don't push through it on a schedule if the child is not understanding.  I think this ties into the grading/mastery paradigm that others are mentioning here.  

I am finding for my youngest that the process of moving through the Algebra I book is going to take much longer. This last chapter we completed we did every single practice problem in the book and then I added more from outside the text because he just wasn't quite solid and I didn't want to move on. In the end, he did get an A on the test, and really, he should have, because by that point we had been over and over the material.   I hope this helps!!

[regentrude]

4 minutes ago, cintinative said:

I'm hoping this isn't off-topic, but one reason that various prior posters keep pushing mastery is that it is SO very important with math.  Algebra I lays a foundation for all the later math that your student will take. So what I have seen on here so many times is--let it take however long it takes for them to understand the material and master it. Don't push through it on a schedule if the child is not understanding.  I think this ties into the grading/mastery paradigm that others are mentioning here.  

and not just that, but also for chemistry and physics.
Students fail college chem because they never understood fractions and proportions.
Students fail college physics because they are weak in basic algebra and cannot focus on the physics concept since they struggle so much with math that, at that point, should be automatic.

[BusyMom5]

My kids don't really know how I figure their grades,  so the test is just something we do at the end of a chapter or every so many lessons in math.  I had one who struggled a lot and phrased tests as a benchmark for the teacher (in public school or me) to be sure that I had taught the lesson well. If she doesn't pass the test, it means I did a poor job teaching it so I have to come up with a different approach to the information.    

In math, she does the test,  I grade it.  She has to redo mistakes for half credit.  If I notice it's all little errors,  but she does have the right form, we move on.  That shows she knows the content but got a bit sloppy and forgot an exponent or something.   If I notice that problems were not approached correctly,  then we go back and reteach.  

Daily homework- I do sit here every day and help with any problem she gets wrong.  She has the answer key and checks it herself.  If she can't get it, then I help.  I do not give a grade for homework- as I expect every question to be answered correctly with or without help,  but I do give completion points at the end of the year- usually 500pts (equivalent to 5 tests), and 100pts for writing math notes all year.  Each test is 100pts, usually 20 tests-

~2000pts tests

600pts homework and notes

 

 

[Not_a_Number]

2 hours ago, cintinative said:

I'm hoping this isn't off-topic, but one reason that various prior posters keep pushing mastery is that it is SO very important with math.  Algebra I lays a foundation for all the later math that your student will take. So what I have seen on here so many times is--let it take however long it takes for them to understand the material and master it. Don't push through it on a schedule if the child is not understanding.  I think this ties into the grading/mastery paradigm that others are mentioning here.  

I am finding for my youngest that the process of moving through the Algebra I book is going to take much longer. This last chapter we completed we did every single practice problem in the book and then I added more from outside the text because he just wasn't quite solid and I didn't want to move on. In the end, he did get an A on the test, and really, he should have, because by that point we had been over and over the material.   I hope this helps!!

Yep! And moreover, don't hesitate to review arithmetic if you run into issues with it when doing algebra. Algebra is very much built on arithmetic, and in my opinion, understanding of algebra is simply a generalization of one's understanding of arithmetic. 

[kristin0713]

I didn't read all the replies, but this is what I do.  We are using Christian Light for Algebra 1.  I do 50% daily work (120 assignments), 25% quizzes (there are 20), and 25% tests (there are 10).  Her daily work is pretty much an automatic 100% because I require her to fix everything and do more work on things that are harder for her.  

[EKS]

1 hour ago, Not_a_number said:

Yep! And moreover, don't hesitate to review arithmetic if you run into issues with it when doing algebra. Algebra is very much built on arithmetic, and in my opinion, understanding of algebra is simply a generalization of one's understanding of arithmetic. 

This is the great thing about homeschooling. It's very forgiving because if you're hands on with your teaching, you actually have the opportunity to see where these problems are arising and fix them in real time.  this is why I think people shouldn't worry so much about gaps when they're homeschooling. And I agree with you about algebra being a generalization of arithmetic. This is why I always think of Algebra 1 as being the culmination of elementary school arithmetic rather than the beginning of high school math.  Of course that never stopped me from giving high school credit for Algebra 1!

[Not_a_Number]

1 minute ago, EKS said:

This is the great thing about homeschooling. It's very forgiving because if you're hands on with your teaching, you actually have the opportunity to see where these problems are arising and fix them in real time.  this is why I think people shouldn't worry so much about gaps when they're homeschooling. And I agree with you about algebra being a generalization of arithmetic. This is why I always think of Algebra 1 as being the culmination of elementary school arithmetic rather than the beginning of high school math.  Of course that never stopped me from giving high school credit for Algebra 1!

I agree with you there 🙂 . It's very much a "Have you understood how things work? Well, here's a way to write that down in general." If a kid is ready, it's not a big jump. 

[Ausmumof3]

9 hours ago, EKS said:

Easy--you structure your homeschool so that they can't be "done" until the understanding (and fluency) is at mastery.   

That said, I have them take tests in math because I think that test taking is an important skill.

My kids like to “finish” a math book each year.  That’s my problem.  My oldest has been doing extra math at night because he doesn’t want to get “behind”.

also I guess like I’ve hit the long division thing in Singapore and youngest isn’t getting it well.  I can’t see the point of sticking in this subject to mastery at this point because he not developmentally ready for it.  But the second half of the book is measurement conversions, time, geometry all of which he understands and can move through.  So it makes more sense to me to move forward and tackle those segments then come back to the long division later.  He can mentally do all the division required for the other math in the rest of the book he just can’t manage the algorithm at this point.  
 

Also with my dd she can demonstrate apparent mastery.  sail through the exercises and the reviews. Explain the concept. Hit the topic three weeks later and have no idea what she’s talking about.  It seems best to me to keep moving but circle back and redo what’s been lost or forgotten.

[EKS]

8 minutes ago, Ausmumof3 said:

also I guess like I’ve hit the long division thing in Singapore and youngest isn’t getting it well.  I can’t see the point of sticking in this subject to mastery at this point because he not developmentally ready for it.  But the second half of the book is measurement conversions, time, geometry all of which he understands and can move through.  So it makes more sense to me to move forward and tackle those segments then come back to the long division later.  He can mentally do all the division required for the other math in the rest of the book he just can’t manage the algorithm at this point.  

I totally agree!  With both kids I simply had them do a few long division problems alongside the new material.  They weren't "done" with long division, but that didn't mean that they couldn't move forward with other things.

[Farrar]

Seconding everything that 8 and Regentrude are saying here. My kids understand that if they finish the work to satisfaction - and in the case of math, that involved redoing it until it was mastered - then they get an A. Simple as that.

I don't find this all that confusing or difficult to put on a transcript. My kids have not found it a disincentive either. I understand that grades can also be an incentive - they have had outside classes and I let the grade be the grade in those cases. But for anything I teach at home, I honestly see this as core to how we teach and learn.

[EKS]

9 hours ago, Farrar said:

Seconding everything that 8 and Regentrude are saying here. My kids understand that if they finish the work to satisfaction - and in the case of math, that involved redoing it until it was mastered - then they get an A. Simple as that.

This.

[Not_a_Number]

16 hours ago, Ausmumof3 said:

also I guess like I’ve hit the long division thing in Singapore and youngest isn’t getting it well.  I can’t see the point of sticking in this subject to mastery at this point because he not developmentally ready for it.

Just one thing: I wouldn’t treat it as developmental, I’d treat it as sequential. It’s entirely possible that there’s a missing concept here. I’d probably do partial quotients for a bit and talk division out — it’s the trickiest operation. 

[EKS]

11 minutes ago, Not_a_number said:

I wouldn’t treat it as developmental, I’d treat it as sequential.

This a million times!  There is nothing developmental about the acquisition of intellectual skills.  Piaget was wrong.  Instead, I'd argue that what looks "developmental" is really just a combination of prerequisite skills being in place and the child's absolute intelligence at any given time. 

[2_girls_mommy]

We take the same approach as 8fillstheheart. I don't keep grades and percentages. At the end of the course, I know how much effort was put into it and what they are capable of. My odd took a year and a half on an Algebra text. I still only gave her a B. It was mostly due to effort. We went back over things and she could still never do a quiz at the end of a chapter and get above a B because she had a mindset against it.  So she was a B student in math for our homeschool. Her standardized tests reflected what I gave in every subject when we began taking them. She didn't enjoy it, and didn't put her full effort into it. When she began taking ACTs and other national exams and got really amazing (perfect) scores in language related subjects, she knew she had a chance at some real scholarships. So it was important to her to get that math score up so that she was competitive. So she redid an entire Algebra 2 course, redoing every quiz in the course on her own to study for her next round of ACTs. She upped that math score by 7 points which put her in an amazing spot. She got some national honors, interviewed with some very selective colleges, and went to our state school as an honors student with almost full scholarships. Because she had goals of what she wanted to do, she worked even in that subject that she liked the least to get her where she wanted to go. So our approach has worked well. And I did have to write up very detailed course descriptions and grade explanations for her college applications. (She was waitlisted at a national top ten school, and was a Questbridge National College Match finalist so we did ok.) All accepted our very nontraditional way of doing school because of the results it produced. I have always had confidence in the way we school, even though others around me are shocked that we don't do everything in a text and on a timeline as a course. I have had people around me question our methods even in the homeschool world and assume we are unschoolers or not interested in higher education. But it is quite the opposite. I see education very differently than the traditional approach. And it works.  She is making an A in her first college math course this semester. She made As and the president's list during her senior year as a concurrent enrollment student too. 

We taught how to prepare for exams and timelines differently than replicating the same process over and over, year in and year out. We did big projects with scouts where they had to present before a board of alumnae and had timelines and goals and sometimes got turned down and not approved. They did outside competitions and had jobs and volunteer positions in the "real" world. So there was plenty of learning responsibility and planning. 

 

[Ausmumof3]

6 hours ago, Not_a_number said:

Just one thing: I wouldn’t treat it as developmental, I’d treat it as sequential. It’s entirely possible that there’s a missing concept here. I’d probably do partial quotients for a bit and talk division out — it’s the trickiest operation. 

Yeah we can do that.  It’s keeping track of the where to write what bit that’s the issue mostly.  None of my kids like writing steps in math (still having arguments with ds14 over it!).  But a bit more practice with mental division might be good too.  I have been through that thing of trying to teach a concept a million ways, letting it go and then having it sink in really easily later as well. 

 

[Not_a_Number]

1 minute ago, Ausmumof3 said:

Yeah we can do that.  It’s keeping track of the where to write what bit that’s the issue mostly.  None of my kids like writing steps in math (still having arguments with ds14 over it!).  But a bit more practice with mental division might be good too.  I have been through that thing of trying to teach a concept a million ways, letting it go and then having it sink in really easily later as well. 

That's why I don't teach math, lol. I give definitions, I discuss math, I give math problems, but I tell kids how to do things quite rarely. 

[Jann in TX]

When I homeschooled my oldest dds I worked for mastery.  I did not officially test them until they began Algebra 1.  I absolutely knew if they needed to camp out or move on with a concept.  When they got to Algebra 1 and we tested if the grade was below a B we spent more time on that concept. (We ALWAYS re-worked any missed problem together and worked a few more of the same type as practice even if they scored an A...).  This meant that oldest dd (learning differences) took 2 years to get through Algebra 1 and 2 years to get through Algebra 2 (her only high school maths!)-- she ACED her College Algebra class-- only college math class she needed for her degree!  Middle dd did great in all of her college maths.

Now (since I AM the family college plan!) I teach small group math classes.  I have to be accountable to students, parents AND some charter schools that I'm a vendor for.  In my classes homework is worked for mastery-- students/parents have access to all answers and if a student misses a problem it gets re-worked OR if they are stuck they email me and I help.  I give short quizzes --those I grade-- a few times each chapter for accountability-- these are 15-20% of the semester grade.  I do allow retakes on quizzes if grade is below the B level and keep the higher grade for incentive (retakes are different versions in same format).  Tests are the rest of the grade and I grade their work (steps) as much as the answer.  I will occasionally offer a test retake-- my program if fluid-- each chapter building on previous material-- so chapter mastery is important.

I RARELY give partial credit.  I've found that when I do this I have students who continue to make the same errors over and over again.  Instead I teach my students how to look for the errors in their problems and give them strategies to break bad habits (like dropping negatives). The fact that they know that the worst thing that can happen when they take a quiz or a test is that they have to meet with me in a one-on-one tutorial, practice a bit more then take the quiz/test again helps with most of the test anxiety (that is actually pretty common in teens).  I've taught this way for the past 18 years (online small group classes) and it has worked well for me and my students.

All this is to say that the strategies used in one-on-one teaching are different than the strategies used in a classroom (synchronous learning).

 

 

 

 

[EKS]

16 minutes ago, Jann in TX said:

I RARELY give partial credit.

Interesting. 

I see your point about needing to inspire students to get beyond making the same silly errors again and again, and in a classroom situation this may be one of the only ways to do that.  On the other hand, I want the test grades to reflect my students' understanding of the material, and if I don't give partial credit, just a few silly errors on, say, a 10 problem test have the potential to really mess with that.  

I've found that if students are making a lot of silly errors, it usually means that they haven't fully integrated the new material and need more practice to make whatever it is more automatic.  Since I'm teaching one-on-one, upping the number of homework problems is easy.  If I had an entire class to teach, this approach might not work as well.

I have also told students that if they do a particular bad thing (that they've been doing over and over) on a test that I will take off all points.

[Reefgazer]

I did not grade homework at all; I considered it practice work.