Anonymous wrote:

OK. At our MCPS school (in the US) in 2nd grade, the kids ARE given the option to use pictures, formulas, or diagrams. As the teacher who teaches at MCPS (in the US) says.

Do you disagree with the idea that if you can't explain the concept, you don't understand the concept?

In 1st and 2nd grade, kids were allowed to draw pictures, or diagrams but were discouraged from using formulas. In 3rd grade, they are specifically asked to write an explanation using language and sentences.

I do disagree with the statement that if you can't explain the concept, you don't understand the concept. This is plays out in many, many fields. A great violinist hears, feels, and understands fully the concepts of pitch, harmony, tones etc. This same violinist may not be able to write an essay explaining in sentences how they play so well. A english major or music history major may be able to write a wonderful essay comparing and contrasting or explaining this but can't play a simple tune. An artist may be able to construct beautiful compositions but again is far less successful in translating this into a writing skill to explain what they already know and have learned. There is no value in forcing everything to conform to a language assignment approach.

Equations, numerical values, and symbols are the "language" of math. Proofs and theorems, as well as simple equations, do explain math. There are many ways to go deeper in math at the elementary school level and to show how math is a serious of related interactions.

MCPS's interpretation that understanding problem solving means that you can write essays or explain in English sentences how math works is just plain wrong. You don't approach or teach math the same way you approach language arts. You don't teach math as if you are afraid of it and want to avoid numbers and equations.

Anonymous wrote:

I do disagree with the statement that if you can't explain the concept, you don't understand the concept. This is plays out in many, many fields. A great violinist hears, feels, and understands fully the concepts of pitch, harmony, tones etc. This same violinist may not be able to write an essay explaining in sentences how they play so well. A english major or music history major may be able to write a wonderful essay comparing and contrasting or explaining this but can't play a simple tune. An artist may be able to construct beautiful compositions but again is far less successful in translating this into a writing skill to explain what they already know and have learned. There is no value in forcing everything to conform to a language assignment approach.

OK. At our MCPS school (in the US) in 2nd grade, the kids ARE given the option to use pictures, formulas, or diagrams. As the teacher who teaches at MCPS (in the US) says.

Do you disagree with the idea that if you can't explain the concept, you don't understand the concept?

Anonymous wrote:

Another Ph.D. who earns her living from math here -- disregard this PP. If you can't explain the concept, that means you don't really understand the concept. And, as the MCPS-teacher PP says, you don't have to write "3 explanatory sentences". There are lots of different ways to explain it.

Sorry, we're a two Ph. D household and I agree with the earlier poster. This is bad and a perfect example of why the US ranks so low in math compared to other countries. If you have county level education majors who do not understand math writing the math curriculum, you end up with language curriculum not math. They really do not understand the subject and can only translate it in terms that they can comprehend. Its a mess.

At our school in the 3rd grade, the kids are not given the option to use pictures, formulas, or diagrams to explain the answer. The worksheets and assessments ask the student to explain it and gives them several lines (clearing indicating text and sentences). The kicker is that the teacher corrects the spelling, grammar, and punctuation!

Another Ph.D. who earns her living from math here -- disregard this PP. If you can't explain the concept, that means you don't really understand the concept. And, as the MCPS-teacher PP says, you don't have to write "3 explanatory sentences". There are lots of different ways to explain it.

Anonymous wrote:Suggestion from a Ph.D. who earns his living from math: Don't worry about it. Make sure she understands the concept, and is able to solve the problems. You should be able to say if she understood or not without forcing her to write 3 explanatory sentence why 10 x 10 = 100. Otherwise you will just make her hate math. MCPS math curriculum is ridiculously easy. And yet it insists students to write and write and write to "show their understanding" of primitive concepts.

Anonymous wrote:Suggestion from a Ph.D. who earns his living from math: Don't worry about it. Make sure she understands the concept, and is able to solve the problems. You should be able to say if she understood or not without forcing her to write 3 explanatory sentence why 10 x 10 = 100. Otherwise you will just make her hate math. MCPS math curriculum is ridiculously easy. And yet it insists students to write and write and write to "show their understanding" of primitive concepts.