Reys Chapters 8 & 9

Reys: Chapter 8

“As children develop rounding skills, they should come to realize that rounding rules may vary and are not universal. ”

Reys discusses in the rounding section that many textbooks explain rounding in different ways. Reys gives the example of how one text explains changing the 5 to 0 and increasing the previous digit by 1 and another text says change the 5 to 0 and if the digit preceding the 5 is even, leave it alone and if the digit preceding the 5 is odd, increase it to the even digit. This can be a problem with some numbers like 85 because in one instance it would be 90 and another would be 80. In the class I am observing for rounding I noticed they had a sound and exactly four rules. The song goes over how if the number is more than five you round up and if its four or less you let it rest. I noticed that the third graders really caught on quickly because the song helped and the four rules are simply step by step. One rule include underlining the number to the right of the circled number. You circle the number you will be rounding.

Reys: Chapter 9

Focus Question # 3: What three distinct types of situations lead to subtraction? What four types of structures lead to multiplication?

The three distinct types of situations that lead to subtraction are separation problems, comparison problems, and part-whole problems. The four types of structures that lead to multiplication are equal-groups problems, comparison problems, combinations problems, and area and array problems.  Reys mentions that the separation problems are usually the easiest problems for students because they look at this as take away problems. The comparison problems involve matching the numbers where one will cancel another basically crossing out pairs and seeing what numbers are left.  For part-whole problems nothing is being added or taken away instead you will only have a static situation that involves parts and a whole.

Vaughn Chapter 16 & Reys Chapter 15

Vaughn: Chapter 16

Focus Question #4: What are some effective ways to help students become active learners in the classroom?

Some really effective ways that students can become active learners is having opportunities for students to work in pair share or learning groups. I find this way really effective because I myself as a student learn more and get more perspectives when we work as a group. Another way that Vaughn mentions is giving the students guidelines for note taking. It is important to listen to understand instead of listening for every word to write down. Notes will only be effective when you tailor them to yourself. A helpful hint can be to leave extra space so that when you go back there is room to add more information that can be helpful for your own understanding.

Reys : Chapter 15

Focus Question # 1: Why should the elementary mathematics program include geometry?

Before I began reading I tried answering this question with what I thought would be the reason as to why it is important to include geometry in elementary mathematics. My first though was that it helps students connect real life to mathematics. This was one of the reasons that Rey’s textbook mentioned because there are so many three-dimensional objects in the world that children encounter. Rey’s textbook also mentions how geometry opens doors to many cultures because many cultures have different types of architecture and geometric designs that are commonly used in that culture. There are also so many parts to geometry like congruence and similarity that can correlate into other subjects such as science and art when drawing or observing rocks or insects.

Reys Chapters 6 & 14

Reys: Chapter 6

Focus Question # 1: What is the difference between solving problems and practicing exercises?
           
        Reys mentions that the difference with solving problems and practicing exercises is the kind of level of thinking that is involved. With solving problems a higher level of thinking is required versus with just doing exercises the only challenge as Reys puts it is “ doing the computation. Solving problems does not mean doing traditional textbook word problems because a lot of these type of problems are just stories with words here and there not really causing the student to really think critically. From experience with tutoring and even in my own mathematics I have learned to spot the difference between exercises and problems that require solving. The routine problems as Reys calls them are literally just numbers that students can skim through the words and simply add, subtract, multiply, or divide the numbers without really having to think on a higher level. It is not to say that routine problems are not good exercises for students because they can also be used to build algebraic understanding. It is true that so many people underestimate the abilities of children and as a future teacher I have to make sure to provide my students with true problems and those resources needed to be able to solve these non-routine problems. Teachers should introduce problems that will help students survive in the real world as opposed to just problems that are conveniently set up to make the problem easy to compute.


Reys: Chapter 14

“ It is often difficult to get into the minds of children, so having them explain their thinking is crucial.”

            While doing the reading on chapter 14 I stumbled upon this phrase that made me think about how important it is to give students the chance to explain themselves. I actually learned more about math from getting the chance to explain how I arrived to a solution. I can’t remember if in elementary school I had the chance to explain myself, but in high school I did especially when I would help my sister with her math. No one can get into the minds of others; therefore in order to understand what the other has grasped we need to give them the opportunity to explain how they solved the problem and even how they feel about the problem. It could be that a student arrived to the solution in a different way that what the teacher explained and they could get the chance to explain why their way made more sense. This quote does not only apply to math, but I can see it being applied to life. Like I mentioned on Reys chapter 6, children are always being underestimated and it should be our duty as teachers to make sure that our students are active and have the opportunities to make themselves be heard. If we allow for our students to explain their thinking not only could they help themselves, but they can help other classmates and even help the teacher.

Reys Chapters 4 & 10, Vaughn Ch. 15

Reys: Ch. 4
    
"Assessment of Learning" and  "Assessment for Learning"

These phrases from Rey's chapter four really stood out to me because although students will be assessed by the state on their performance it is important to make sure that as teachers we are assessing our students so they can improve on their skills.  The four phases for the classroom assessment process that the book describes are : planning, gathering, interpreting, and using. These phases will be really helpful because in order to know what we need to teach our students we need to see where they are at. We need to see who understands fractions or place value and who has trouble with it. First, the teacher needs to plan what he or she would test and how he or she would test the students. Then the teacher would interpret the information he/she gathered from the test or task he/ she planned.  With the teacher's interpretation of the gathered information of the student;s math abilities the teacher can now plan another lesson or activity.

Reys: Ch. 10

Focus Question # 2: What are some myths and facts about using calculators?

   While reading Rey's chapter 10 some myths I came across where: using calculators do not require thinking, using calculators lowers mathematical achievement, and using calculators always makes computations faster. From personal experience I can say all of these are myths because I've used calculators that I've had to read the manual several times just to change the mode and its wasted me a lot of time. However, I am not against calculators because I am a firm believer in checking your work and using a calculator is such a great tool for checking your work. As for facts I read that sometimes it is faster to compute mentally rather than use a calculator and that calculators do not do all the thinking themselves it requires work from the student. These facts are true because I've seen it several times when younger students I've tutored have tried using a calculator to do a simple addition problem. At first I tell them I know they can do it without the calculator and they insist. They take quite a while just to figure out where the numbers are and the signs that I help them, but in the condition that they will not use the calculator because they agree that using the calculator takes longer.

Vaughn Ch. 15
  

Focus Question #3 What can you do to prepare lessons that engage all students?

To engage all students the teacher should consider all the students needs and be able to plan lesson where the class can participate as a whole, group, or even pairs. Teachers have to see whether the students need extra assistance and where they need extra assistance. A great example that Vaughn's chapter 15 provides is the use of graphic organizers or concept maps. Concept maps can involve participation from the whole class and it can be a fun engaging way to raise questions and investigate if what was written on the concept map was correct or not. Concept maps can also be used for any subject from language arts to science to history and so on.