About 1/3 of the way down, there are examples of three multiplication problems w

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About 1/3 of the way down, there are examples of three multiplication problems with mistakes in their solutions. The text emphasizes how important it is to understand the math well enough to be able to "diagnose" the students' errors, that is, to be able to tell them where their thinking went wrong. In your discussion posting, explain what your diagnosis would be for each of the erroneous solutions. What was the student thinking? How can you correct their thinking?

Teaching Math: More Than Mastering the Numbers NOVEMBER 3, 2014. EMILY RICHMOND JOY RESMOVITS OF THE HUFFINGTON POST FOR EWA Deborah Loewenberg Ball began her career as an elementary school teacher, working for 15 years with a diverse population of students. But math stumped her R50min "That troubled me," Ball said Oct. 21 during her keynote presentation at the EWA seminar on teaching held in Detroit. "I would work really hard on how could l make the math make sense to the students, but on Fridays they would know how to do things and on Monday they would have forgotten." Ball said she realized "something's not right about this." Dean Deborah Loewenberg Ball, University of That block caused her to question her own skills: "Did I of Education, speaks to EWA Michigan School myself, know enough m to be teaching what l was doing?" members in Detroit on Oct. 21, 2014. (Emil Richmond Ball, now the dean of the University of Michigan School of Education, is using the insights she gleaned as an elementary teacher to improve the overall teaching profession, and tackle what sees as its major problem: "We have no common standard of performance for the individual person before they become licensed to teach." (Elizabeth Green's new book, "Building A Better Teacher" documents Ball's story in great detail.) She's trying to create a new bar for entry to the field After Ball recognized the gap in her own education, she set out to improve her math teaching. She tried to learn more math content, because she "thought that was part of the root issue." Ball determined the core issue was "teachers knowing enough subject matter, and very different from what most teachers think the problem is In other words, teachers don't only need to know math. They need to understand the underlying concepts of math so deeply that they can identify the steps students are missing just from looking at their erroneous solutions. For example, teachers must be able to immediately understand what went wrong in students' methodologies when they came up with the following solutions to these multiplications problems

Explanation / Answer

a.

49×25= (50-1)(30-5)=1500-30-250+5=1425 but he wrongly put 1485

b.

49×25=20×9 + 5×9=225

20×4 +5×4=100

so add 225+100=325

c.

49=40+(10-1)

now multiply this number by 25 to get

(40+(10-1) ) 25= 1000+250-25

but here the student wrote wrongly +25

so it became 1000+250+25= 1275

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