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"The wonderful thing about standards ...." There are several ways to teach children to multiply. Which is standard? Indeed, different places privilege differen

"The wonderful thing about standards ...." There are several ways to teach children to multiply. Which is standard? Indeed, different places privilege different algorithms. I mentioned the counting-intersections method. https://en.wikipedia.org/wiki/Multiplication_algorithm https://en.wikipedia.org/wiki/Multiplication_algorithm says England and Wales use the grid method. As the first document at Equitable Math points out, "The point should be to have a dialogue about their process and their learning, not require every student to follow the exact same path to the right answer. ... The child of immigrants might have learned a different way to solve a problem because that’s how their parents were taught where they grew up. If we just tell that student their way is the wrong way, we risk turning them off to math for life." So if someone from the UK comes to the US, and uses the grid method to get the right method, instead of long multiplication as I learned it in the US, and the teacher gives them a zero and says it's the wrong way, because it's not the standard way .... is that really good pedagogy? Or is it more likely to discourage the student? Or, a couple months back there was a link here about indigenous students in Alaska who natively speak a base-20 language. As I recall, it was more effective for them to learn math in base-20, and then learn base-10, than to follow the standard route of teaching math in base-10. Do you really disagree with this viewpoint from Equitable Math, or is your complaint with my pull quotes, which necessarily omits context?

WalterBright 5y ago
I find the very notion of algorithms being "privileged" and that somehow math can be "equitable" weird. I don't see any problem with a teacher saying "this is the algorithm I'm going to teach" and testing them after teaching it. I don't see how that discriminates or hurts anybody. If they know another way, so what? If they can learn that way, they can learn another way. > because it's not the standard way "Because it's not the algorithm I'm teaching" is not unreasonable. I never got bent out of shape by a teacher/prof saying "this is the way we're going to do it." I just did it that way. I wasn't being oppressed.
- eesmith 5y ago
  I noticed you didn't answer my question, so I'll pose it again. Suppose a teacher decides everyone must learn the counting-intersections method in order to learn to multiply. One of the students already knows long-multiplication and can even multiply two-digit numbers in her head. And she thinks that drawing all those lines and counting intersection is a boring, tedious, useless way to multiply. She gets all of the answers right, and is the first to finish. But she gets a zero, because she didn't do what the teacher taught. Is that good pedagogy? Is it teaching mathematics? Is it encouraging the child to learn more math? Or is it (as the text argues), more likely teaching conformity to the power structure, and possibly demotivating the student? The argument is that not everyone is like you; not everyone can fit into the power structures at school which unnecessarily and even subconsciously reflect the dominant culture. The argument is that teachers who are aware of these issues may be more likely to educate a wider range of students.
  - WalterBright 5y ago
    I did answer the question, in my own way, because I do not accept your framing of the issue. Your frame it in provocative and loaded terms like "privilege", "dominant", "pedagogy", "power structure", etc. I don't view mathematics through your lens at all.
    - eesmith 5y ago
      As a reminder, this isn't directly about "mathematics" but "mathematics education". I don't see how you can talk about education without using concepts associated with pedagogy, which is "the theory and practice of learning, and how this process influences, and is influenced by, the social, political and psychological development of learners." (Quoting WP) Can you reframe my scenario with a framing you like? Teacher A wants students to learn principle X. Teacher uses method M to do so. Student B already knows principle X, via method N. Teacher says student's method N is wrong, because it isn't method M, and gives student B a poor grade. Student B becomes demotivated, and doesn't care so much about learning principles Y or Z. Teacher A wants students to learn principles Y and Z. What framing would you use to describe this situation? Do you think teacher A should change their teaching style? In the document I referred to, method M is the standard way taught in the US, method N is the standard way taught in another country, and student B is an immigrant child who learned method M from B's parents before teacher A taught it in class. In my scenario, method M is a very visual technique for multiplication used for early learners, and method N is the standard way taught to more advanced learners in the US.

WalterBright 5y ago

I find the very notion of algorithms being "privileged" and that somehow math can be "equitable" weird. I don't see any problem with a teacher saying "this is the algorithm I'm going to teach" and testing them after teaching it. I don't see how that discriminates or hurts anybody. If they know another way, so what? If they can learn that way, they can learn another way. > because it's not the standard way "Because it's not the algorithm I'm teaching" is not unreasonable. I never got bent out of shape by a teacher/prof saying "this is the way we're going to do it." I just did it that way. I wasn't being oppressed.

eesmith 5y ago
I noticed you didn't answer my question, so I'll pose it again. Suppose a teacher decides everyone must learn the counting-intersections method in order to learn to multiply. One of the students already knows long-multiplication and can even multiply two-digit numbers in her head. And she thinks that drawing all those lines and counting intersection is a boring, tedious, useless way to multiply. She gets all of the answers right, and is the first to finish. But she gets a zero, because she didn't do what the teacher taught. Is that good pedagogy? Is it teaching mathematics? Is it encouraging the child to learn more math? Or is it (as the text argues), more likely teaching conformity to the power structure, and possibly demotivating the student? The argument is that not everyone is like you; not everyone can fit into the power structures at school which unnecessarily and even subconsciously reflect the dominant culture. The argument is that teachers who are aware of these issues may be more likely to educate a wider range of students.
- WalterBright 5y ago
  I did answer the question, in my own way, because I do not accept your framing of the issue. Your frame it in provocative and loaded terms like "privilege", "dominant", "pedagogy", "power structure", etc. I don't view mathematics through your lens at all.
  - eesmith 5y ago
    As a reminder, this isn't directly about "mathematics" but "mathematics education". I don't see how you can talk about education without using concepts associated with pedagogy, which is "the theory and practice of learning, and how this process influences, and is influenced by, the social, political and psychological development of learners." (Quoting WP) Can you reframe my scenario with a framing you like? Teacher A wants students to learn principle X. Teacher uses method M to do so. Student B already knows principle X, via method N. Teacher says student's method N is wrong, because it isn't method M, and gives student B a poor grade. Student B becomes demotivated, and doesn't care so much about learning principles Y or Z. Teacher A wants students to learn principles Y and Z. What framing would you use to describe this situation? Do you think teacher A should change their teaching style? In the document I referred to, method M is the standard way taught in the US, method N is the standard way taught in another country, and student B is an immigrant child who learned method M from B's parents before teacher A taught it in class. In my scenario, method M is a very visual technique for multiplication used for early learners, and method N is the standard way taught to more advanced learners in the US.