The Student’s Role in Formative Feedback Cycles

The Student’s Role in Formative Feedback Cycles

Nicole Rigelman, Portland State UniversityTeachers of Teachers of Mathematics Conference

September 6, 2013

Session Overview Engage in a mathematical task and discuss

strategies (we’ll return to this later) Examine a research-based vision for instruction and

assessment Connect to case of a third grade classroom

Classroom Culture Focused on Developing Mathematicians Selecting Tasks to Ensure Quality Data Feedback and Revise Cycles

Consider implications for our instruction and assessment practices

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.

http://www.corestandards.org/Math/Practice/MP3

Brownie Sharing TaskThe sisters decided to each order a different brownie so they could share. Gabrielle ordered a white chocolate brownie and Isabella ordered one with peanut butter chips. Gabrielle said that the piece Isabella gave her was not half of her brownie. Their cuts are shown below. Did they each get a fair share of each other’s brownie? How do you know?

Gabrielle’s Brownie Isabella’s Brownie

Common Core Connections 3.G.A.2 Partition shapes into parts with equal

areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

http://www.corestandards.org/Math/Content/3/G/A/2

http://www.corestandards.org/Math/Content/3/G/A/2

http://www.corestandards.org/Math/Content/3/NF/A/3

The Student’s Role in Formative Feedback Cycles

• Solve worthwhile mathematical tasks that are cognitively demanding and connected to appropriate standards.

• Engage in mathematical practices such as:• observe patterns, • make use of structure, • model mathematics and translate

among various representations, • engage in a process of conjecturing

then justifying and generalizing those conjectures.

Students Engage in Mathematical Thinking and

Reasoning

• Understand the learning goals /intentions and the criteria for success.

• Ask genuine questions to deepen their understanding.

• Critique their thinking and the thinking of others.

• Engage in self- and peer-assessment.• Use feedback as opportunity to grow

and improve.

Students Own Their Learning

Classroom Culture Focused on Developing Mathematicians

Students made the conjecture “an even plus and odd is always an odd.”

The teacher asked the students to decide if they agree with this conjecture.


8 7


27 + 100 = 127 (odd) How do you know?

Because 27 is odd, and 100 is even

How do you know 27 is odd? How do you know 100 is even?


500 + 9999 = 10499 (odd) How do you know?

Because 9 is odd


Because we wanted to move students toward proof that was based on more than just a memorized fact, we decided that the next day’s lesson should focus more on how even and odd numbers look, how the structure can support you in deciding if the sum is even or odd.

We wanted students to come to see representations as a potential tool in developing convincing arguments.

Developing Classroom Culture through Written Feedback - S’Mores Problem

I made s'mores with my daughter and had some leftover chocolate for next time! How much chocolate is leftover? [The teacher showed the students the left over chocolate that was equivalent to 1 ½ or 3/2 chocolate bars.]

I think being a mathematician is when you are pretty good at math

and when you really show work when you are doing something. Like if you are doing fractions or something, you use a model or a number line to show

your thinking.

It is someone who knows how to learn math

well.

Being picky about what models you are

using, how your jumps are on the

number line, when you are measuring, starting at zero, and

things like that.

It is about being confident in yourself and

knowing you can do it. It’s not

about talent, no matter how smart you are, you can

work on it, rely on it more, and do it

more. It is not about being the smartest kid in class. It is

someone who relies on tools, no uses tools, trying to decide if

someone else is right or trying to prove your thinking to them.

Selecting Tasks to Ensure Quality Data – The Brownie Sharing Task

The sisters decided to each order a different brownie so they could share. Gabrielle ordered a white chocolate brownie and Isabella ordered one with peanut butter chips. Gabrielle said that the piece Isabella gave her was not half of her brownie. Their cuts are shown below. Did they each get a fair share of each other’s brownie? How do you know?

Gabrielle’s Brownie Isabella’s Brownie

Feedback & Revise Cycles

Sometimes I feel kind of sad about that, like when she writes you a

question. Sometimes it’s like “Wow, you did it” and sometimes it’s like

“You need to rethink this.” It reminds me of being behind in my work

because I have to do it the next day.I think it is pretty

good. She doesn’t say that we’re wrong, she says rethink. I might

need to be more precise or to prove a little bit more. Maybe I need to match my

models.

I like getting feedback because when you get it you get to fix what you

did wrong. Well not wrong, you just need to rethink. I like it because

you get to know how other people think about your work.

It is like having a conversation with

the teacher. If I don’t understand

something, I can ask a question and she will write me a note or a question that will help me think

about it some more. Or we will have a

conversation about it.

I think it helps because when you go to a test she does not

give you feedback but by then you kind of know a lot. When you

have a chance to fix your stuff you notice what you are missing

and I think that helps a lot.

Implications What are implications for instruction and

assessment practices in your courses? as you support teachers? other?

The Student’s Role in Formative Feedback Cycles

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