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While Chapters 4-5 from Designing Effective Mathematics instruction focused on very basic math skills such as counting and place values. I can still see the value for my 7th grade students. More specifically, when it comes to understanding place value. I think the recommendations presented in the text can be stretched for using decimals. A large problem my students faced this year was performing operations with decimals without the use of a calculator due to the fact that they simply lacked a fundamental understand of decimal place values. I think that it would be helpful for my students to take a step back just to focus on place value with decimals that way they can have a better understanding of not only how to perform operations with them but also how to properly read decimal numbers.

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In the chapters 4-5, the author discussed very VERY basic mathematical skills, such as counting and place value identification. My biggest takeaway is that learning how to count is much more complex that I had ever imagined. Growing up and learning how to count, I never would have thought much about the sequence in which I learned certain mathematical tasks. It stands to reason that one must learn how to count FROM a specific number before one can think about multiples through skip counting, however I never would have thought about how discrete these steps must be.  It seems that this could be used as a diagnostic tool for scholars with LDs in math to learn their levels of mathematical understanding.  We have had 8th grade scholars who only demonstrate a 3rd grade level of mathematical understanding, and this count have been a quick diagnostic to help us understand her skills much more quickly (i.e. asking her to skip count by 5s and seeing how high she could go).

Though I am more familiar with place value, I have only taught students about place values that are smaller than 0 (tenths, hundredths, thousandths, etc.). What struck me most here is that the sequence used to teach and understand large place values. Students must be able to identify numbers from an oral prompt (i.e. say "fifty-six hundredths" and the student is able to write .56"), as well as correctly align place values when solving a number sentence.

In terms of remaining questions, I do not have any at this time. This is frankly because the mathematical understandings that have been highlighted thus far are focused around skills that scholars must master in elementary school. However, it does impart to me the necessity ensuring scholars are actually mastering concepts and strategies in math before moving on to new content. Each skill immediately builds on the previous one, and thus a gap in any one understanding would severly impact a scholar's ability and achievement in math overall. A student cannot go into 6th grade without having a strong understanding about relationships between numbers and how they work (i.e. multiplication by a whole number, multiplication by a fraction/decimal both larger and smaller than 1, etc).

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Chapters 4 and 5 from Designing Effective Mathematics Instructions is about counting and place values.

I like that these chapters focus on basics. With the push towards mastering complex concepts in the common core, stuff like this often gets lost.

I also appreciate that the chapter points out the importance of pacing. While it is important to review the basics, students often feel like it is insulting. Keeping the energy up helps counteract this.

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Michelle Yaghoubzadeh's Response to Chapters 4&5

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Michelle Yaghoubzadeh's Response to Chapters 4&5

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The major takeaways from Chapters 4 and 5 from Designing Effective Mathematics Instruction about Counting and Place Values is the importance of them in multi-step and more challenging problems. Counting is the basis to most math operations.

Symbol Identification is also a very important basis to math solving. To introduce Place values, students must learn the differing names of values and what they mean. This is an integration of literacy into math. One way to introduce this that is beneficial to students is to use the column method.

When I taught math last year, I used strategies from these chapters when building instruction. Specifically when using place values, and introducing money.

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Alex Bauer's Response:           Since I am a high school math teacher, it was very interesting to read how to teach math to young children. Chapter 4 discusses counting and recommends that students use visuals such as pictures of objects or even physical objects. As students learn more difficult math, math visuals are even more helpful as the mathematical instruction gets more complex.In chapter 5, the book discusses the importance of symbol identification and teaching place value skills. These skills also require visual representation to help students solve the mathematical problems. I agree with the authors when they state, "Equation reading is a prerequisite skill for problem solving and learning math facts" (p. 52). Students must be able to read the equation, identify the numbers and know the symbols before solving an equation. Again, it is still very helpful for students to use visuals to help them solve more complex and difficult math problems. As I read these chapters, I realized just how important it is for students to learn the proper math concepts and solving techniques when they are younger. It is so important for students to get a good math foundation so they can build on the math and learn new math concepts and instruction as they get older.  

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Alex Bauer's Response:           Since I am a high school math teacher, it was very interesting to read how to teach math to young children. Chapter 4 discusses counting and recommends that students use visuals such as pictures of objects or even physical objects. As students learn more difficult math, math visuals are even more helpful as the mathematical instruction gets more complex.In chapter 5, the book discusses the importance of symbol identification and teaching place value skills. These skills also require visual representation to help students solve the mathematical problems. I agree with the authors when they state, "Equation reading is a prerequisite skill for problem solving and learning math facts" (p. 52). Students must be able to read the equation, identify the numbers and know the symbols before solving an equation. Again, it is still very helpful for students to use visuals to help them solve more complex and difficult math problems. As I read these chapters, I realized just how important it is for students to learn the proper math concepts and solving techniques when they are younger. It is so important for students to get a good math foundation so they can build on the math and learn new math concepts and instruction as they get older.  

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One major takeaway from Chapter 4 is that there is a specific sequence that counting skills need to be taught in. From counting by ones to skip counting by larger numbers, there is a method to leading the student to those later skills. This chapter dove into even more of the particular ways teachers teach pronunciation of counting and skip-counting. There's so much that goes into the first level of number instruction that I didn't even think about.

Chapter 5, which covers place value in numbers, explains the process that begins with students identifying single digit numbers and slowly graduates from column to column for each place value that follows. One major takeaway that this chapter, as well as the last one highlighted is that engagement and pacing is still a very crucial part of this instruction. It can be very easy for students to get board or space out when dealing with such simplified concepts, but they must stay readily engaged or they run the risk of not being ready for when the latter numbers and symbols come together to express sentences.

These chapters really made me think about how I connect, not just my lessons, but the different parts of each of my lessons.  We spoke about fluidity of concepts last week, but to me, these two chapters really spoke to the importance of the order in which we explain parts of concepts when they're brand new.
Some questions I have are how to better identify when students are missing the necessary prerequisite for the next concept? While I know we should be monitoring, it's easy for students to slip under the radar and for their misunderstanding to come out later when we're knee-deep into new material. For example, in the middle of chapter 5 (pg. 59) the text talks about teachers questioning students through the number of commas they see and having them identify what the numbers around those commas tell us about the number. However, I've seen firsthand in my 9th graders that students are still not 100% confident in identifying place value. It makes me wonder how their instruction leading up to 9th grade either didn't accurately assess this skill, OR just didn't reinforce it enough through practice.

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Response to Designing Effective Mathematics Instruction

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Response to Designing Effective Mathematics Instruction

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What were some major takeaways from the math reading done to date in Chapters 4-5 from Stein, M , Kinder, D. Silbert, J. Carnine, D. W. (2006)Designing Effective Mathematics Instruction: A Direct Instruction Approach?

What are the implications for your teaching of math?  What questions do you have about the content read so far? Be sure to reference specific points and chapters!