Categories
Arithmetic with Polynomials and Rational Expressions Feedback Rational Expressions

Rational Expressions

IMG_20130331_173311

 

How would you help this student?

Another thought: would this student have made this mistake at the beginning of the problem? In other words, is this mistake more likely to happen as the problem goes on than at the beginning? If so, then what does that say about problem-solving?

Thanks to Anna for the submission!

Categories
Geometry Right Triangles

Special Right Triangles

4 1 2 3

Let’s take for granted that these students don’t have conceptual understanding of the Pythagorean Theorem, because if they did, then they wouldn’t make these mistakes. (I actually think that we need to be more careful with the ways that we toss around phrases like “conceptual understanding” but whatever.)

What do these mistakes reveal about how these kids think about right triangles and the Pythagorean Theorem in the absence of conceptual understanding? Why does this ever make sense to the student?

Thanks to Michael Fenton for the submission!

Categories
Feedback Geometry Quadrilaterals

A Parallelogram is a Rhombus

ASN 6 2 ASN 6

These are some “Always, Sometimes, Never” questions. Like, “Is it always, sometimes or never true that a rhombus is a parallelogram.”

What’s the fastest way to help these students?

(Thanks for the submission, Tina C!)

Categories
Multiplication Numbers & Operations in Base 10

Lattice versus Partial Products

triangleman1

 

I’d love to hear anything that you’re thinking about this in the comments.

I wonder: should we be giving kids explicit guides for these sorts of algorithms at all? Algorithms ought to be patterns in thought. Does a mistake like this begin to make a case against these sort of printed aids?

Thanks to Professor Triangleman for the submission.

Categories
Decimals Elementary School Measurement & Data Money

Money and Decimals

Brown2

 

What strikes me about this piece of student work is how clean and predictable their mistake is.

Is this sort of mistake the rule or the exception? Does a mistake like this reflect the fact that many/most student errors are due to coherent mental models, or is it the rarer exception in a world dominated by stormy minds that fling ideas at math less predictably?

Thanks again to Dionn!

Categories
Fractions Number & Operations -- Fractions

Subtracting Fractions

Brown1

I’ve been reading some constructivist stuff lately, so…

What resources does this student have for refining their understanding of fractions?

(Thanks for the submission, Dionn!)

Categories
Discussion

Shall we close up shop?

time to move on

From “Misconceptions Reconcieved.”

What say you all? How does the quote above relate to this little project? Agree? Disagree? Comments, please!

Categories
Arithmetic with Polynomials and Rational Expressions Feedback Rational Expressions Rational Expressions

Factoring + Rational Expressions

IMG_20130331_171842 IMG_20130331_172201

What’s the fastest way of helping these students?

Thanks to Anna for the submissions.

 

Categories
Linear, Quadratic, and Exponential Models* Quadratic Functions Quadratic Functions Quadratics Radicals

Completing the Square, II

matt owen

 

Matt submits the above, and Matt writes, “I think it’s especially interesting that this student left the mistake on the board even though she had found the correct solutions by graphing in Desmos.  I’m not really sure if she did half of forty, or sqrt 4 and then stuck a zero on it (she wasn’t sure either).”

I vote for “half of 40.” You?

Categories
Linear, Quadratic, and Exponential Models* Quadratic Functions Quadratics

Completing the Square

photo (6)

 

What do you notice in this student’s work?

 

Thanks to Matt Owen for the mistake.