Math.Practice.MP1

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP1:  Make sense of problems and persevere in solving them.

    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

Highlighting Mistakes: A Grading Strategy
Lesson Objective: Encourage students to learn from mistakes
Grades 6-12 / Math / Assessment
Math.Practice.MP1

Thought starters

  1. What does Ms. Alcala mean by "flow through" credit?
  2. Why does Ms. Alcala review her favorite mistakes instead of the correct answers before passing back the test?
  3. How does this grading strategy foster a class culture that values risks and learning from mistakes?
101 Comments

I'm really looking forward to trying this in my 6th grade math classroom!

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Great assessment idea!  Do you use it for homework or just assessments?  I usually don't collect homework and grade it, we go over it together.

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I would LOVE to try this in my classroom. Any suggestions on how to go about this in a science classroom?
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I love this idea! I have been using a major/minor mistake method of giving students some more feedback other than just right or wrong, but I like this method much more. There have been several questions regarding how you calculate the actual grade that you put in the gradebook. I would love to know this as well. epatrick@ecsdnv.net
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Saw this video in a PD and decided I wanted to try it for my music classes. I definitely have the "I didn't do well so oh, well/I'm just not good at music." How do you input the initial grade? I would love to see a how you calculate the grade to go into their grade book. Please reply at denniet90@gmail.com
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Transcripts

  • Highlighting Mistakes: A Grading Strategy Transcript

    Leah: I'm Leah Alcala. I teach seventh and eight grade math.

    Today you're going to see

    Highlighting Mistakes: A Grading Strategy Transcript

    Leah: I'm Leah Alcala. I teach seventh and eight grade math.

    Today you're going to see the way that I have started grading tests.

    "Okay, you guys, right now what we're going to do is get our tests back from Friday."

    I've no longer put grades on tests and my feedback is all in the form of highlighted mistakes.

    "When is the retake for this test?"

    Speaker 2: Friday after school.

    Leah: "Friday after school. How do you find out your grade?"

    Speaker 3: Power School.

    Leah: "You go on Power School tomorrow. It will be posted tomorrow. Here we go."

    For me, I really want every interaction I have with a kid to be a learning moment. What I was finding when I was handing back tests the old way, where I put a grade on it, was kids would look at their grade, decide whether they were good at math or not and put the test away and never look at it again.

    "I want you to look at this next one."

    By not putting a grade on the test I feel like what I'm allowing them to do is wrestle with the math that they produced for me first and think of the grade second. When I first did this the number one question I would get every time I passed back a test is, "What's my grade on this? How many points is this problem worth?" And I had to do a lot of, "Remember, you're grade in seventh grade isn't nearly as important as how much math you learn." So that took a lot of re-framing for them and at this point very few kids will ask me their grade and most of the questions that I get are about the math.

    "I want to show you before we get your tests back some of my favorite mistakes that came up a couple times. They could be from any of my classes. -4 times 2x minus 3 equals 28. I highlighted that 2x equals 7. Tell your group what is wrong with this."

    I am highlighting where their mistake is but I'm not mentioning specifically what that mistake is.

    Speaker 4: If 2x equals 7 then wouldn't it be 7 minus 3 which is 4.

    Leah: Uh-huh.

    Speaker 4: But then -4 times 4 is -16.

    Leah: Not -

    Speaker 4: 28.

    Leah: - beautiful.

    So it becomes part of the classwork of getting a test back to figure out why they made a mistake in this particular step. So I see that now when I give tests back, they're continuing to learn.

    Why did I highlight that X? Padma?

    Speaker 5: Because if X is 3 and then the fractions equal 1.

    Leah: So what should they have written instead? Talk to your group.

    Speaker 6: It would have to be 9 over 3.

    Speaker 7: They forgot what they were covering up.

    Speaker 8: They should have written X over 3 equals 30.

    Leah: Right. So I'm going to hand out your tests. Can you guys look at your mistakes and see if you understand them. If you don't understand them can you talk to your neighbor or me.

    Speaker 9: How'd I get -4? How'd I get that wrong?

    Speaker 10: What'd you put? What was X?

    Speaker 11: Hold on I'm thinking. I'm thinking.

    Leah: When you add negative fractions you have to do it this way or this way.

    Speaker 12: -3 times 5 equals -15. Ah.

    Leah: So you really can't look at the number of highlights and determine your grade. It is much more involved a nuance process of understanding what types of mistakes this kid is making and how important are those mistakes in terms of learning math.

    What happened here?

    Speaker 13: I just did it as a negative.

    Leah: Yeah, you just didn't finish. I almost put that one up. I really like that one.

    I grade the test in two go-rounds. I first read from top to bottom the whole test and I'm looking for the moment the mistake gets made. So it's very important to me that I highlight only the mistake and then I explain to them that the answer they got was actually the wrong answer but it wasn't at that point in the problem that they messed up. So I call it "flow through credit."

    So these are two good examples of "flow through credit." Here's one where they made a mistake early on in the problem but then didn't make any other mistake. So their mistake flowed through the problem perfectly. They only lost points for this. In this problem they made a mistake and then even if I assumed this whole line to be correct, they got this wrong based on this, so they would lose points for both lines of this problem.

    The other advantage is I can highlight things that I wouldn't even take points off for. So for instance, on today's test I highlighted if they didn't write that it was the number of treats that Lucy had baked, but I didn't actually take off any points for that because they're going to be fine going forward. But I wanted to bring their attention to that.

    Leah: Once I've done all of that, I look at all the tests a second time and now I'm looking at the test as a whole and I'm saying what kind of mistakes is this child making? Are there common mistakes that are happening over and over again or are there lots of different types of mistakes?

    How about here?

    Speaker 14: I thought it was adding instead of subtracting.

    Leah: Okay, so similar mistakes there. That's really good.

    If they have something in their mind that works and they're applying that mistake over and over again, I'm not going to take off a point from every problem for that.

    That's an easy mistake for me to fix because we just have to have that one conversation versus if they're just doing random things all over the place. Both of those tests might have a lot of highlights on them but one would definitely have a much higher grade than the other.

    Why is that wrong?

    Speaker 15: Because -15x plus 2x is -13x.

    Leah: Beautiful. Can you fix it from there?

    One piece of advice is that it doesn't take longer to grade tests this way. I think that was a big fear. It is a similar amount of time and it's far more enjoyable.

    I felt highlight happy.

    My hope is that through this strategy they see that studying their mistakes and learning from their mistakes is really what learning is.

    What happened here?

    Speaker 16: It was supposed to be plus -5.

    Leah: Plus -5. Everything else was perfect, including your negative sign. Why is this wrong?

    I allow them to retake the test whenever they want and I'll give them a new version of the test. Often kids need to sit with me a little bit more before they're ready to retake. So they'll come see me at lunch or during advisory and we'll go over it.

    Speaker 17: I really didn't understand it.

    Leah: Oh, do you know what to do now?

    Speaker 17: Yeah. The distributive property.

    Leah: Yeah, why don't you do that right now. This one surprised me.

    Speaker 17: I did it the wrong way.

    Leah: So to normalize the process of making mistakes is very much my goal for these kids. It allows them to take more risks.

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Martin Luther King Middle School
1781 Rose Street
Berkeley CA 94703
Population: 957

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