Developing Measurements

I found this week's reading to correspond very well with last week’s reading. Both articles dealt with measurements in the classroom; however this week’s had more to do with developing measurements. Van De Walle talked a lot about different kinds of units that can be measured; both standard and nonstandard. While reading I began to wonder which type of measurement was more beneficial early on in a child’s development (standard or nonstandard). Part of me things it would be difficult to teach very young students what a pound is, or how much volume something has, whereas teaching them its about as heavy as a brick would be more concrete in their mind and would allow students to relate their learning to the real world. On the other hand, I think it’s always beneficial for students to learn vocabulary and terms from a young age. In my classroom I see more standard units of measurement when teaching math, however I’m not fully sure if all the students are understanding the concepts. I believe this comprehension should be assessed more by my CT.
Another area of measuring Van De Walle brought up was estimating. I thought this went really nicely with what we have been doing in class these past few weeks, and especially last week. I think estimating can be a very effective tool, but only when then initial concept has been mastered. I think it will do more harm teaching students how to estimate before they are 100% confident in their ability to solve the problem in full. Some students may use estimating as crutch, and never learn how to fully solve a problem and get the exact answer. I have yet to see any estimating strategies in my kindergarten class and think it is for the best that they have not learned it yet. Some students are beginning to learn very basic addition problems, and I think they will need to develop addition and subtraction skills before they learn how to estimate.

Navigating through Measurement

The article I decided to focus my post on this week is the Navigating through measurements because it particularly pertains to grades 3-5, which are the grades I hope to one day teach. The article started off by saying “Measurement is one of the most fundamental of all mathematical processes” and I couldn’t agree more. I see this a lot in my placement, being in a kindergarten classroom I see the majority of math time being spent on simple counting routines. Every day the go over the calendar and count how many days they have been in school. They represent this number using money (dollars and cents) along with fish (because they are the “fish room”) and with sticks that they count and separate out by hundreds, tens, and ones. One thing I found interesting while reading was “instruction during grades 3-5 places more emphasis on developing familiarity with standard units in both customary (English) and metric systems.” I know I am in kindergarten and perhaps that’s why I don’t see any instruction on the metric system, but I was wondering if Laruen or Gabrielle have seen in being taught in their placements, and if so how important or how much of a role does it have? I think we should start teaching students the metric system for an early age, perhaps even earlier then 3rd grade, what do you guys think? The article also mentioned “children in prekindergarten through grade 2 should have similar hands on experiences to lay a foundation for other measurements concepts.” I agree with this statement and see it in my placement. There is a center during math time that has a large scale and the students are able to make hypothesis on what they believe will be heavier. I thought this was a really center for students to do, because it is a more fun approach to learning about mass and weight without dealing with such large concepts. What evidence of this do you guys see in your placements?

Mistakes

In reading student mistakes, I found it very interesting that students start to work with place values in or before kindergarten and continue to work on this idea through third grade, and sometimes beyond. This is a complicated idea that many students have trouble with and it is important to help them understand this concept by moving from concrete to abstract examples. There are many students in my placement that are having much difficulty with place value. They are in second grade, and it is frustrating for both them and me to learn/teach them the essential ideas one needs to know about the importance of place value.
I also really enjoyed reading the Value of Mistakes article. The authors say that "mistakes are catalysts for learning, or springboards for learning." I really enjoy both of these sayings, because it is very true that mistakes are very imperative to learning. I liked how Mrs. Phillips changed her practices from warning her students about possible future mistakes to giving them a solved problem with mistakes and asked them what was incorrect and to solve the problem correctly. "Rather than warn students about common mistakes as she has in the past, her new approach allows students to value the work of correcting errors by accepting ownership of the common mistakes and the reasoning processes used to overcome them." "Teachers should allow students to work through erroneous thinking as they would in a problem solving situation, that is, with minimal learning guidance." I learned this last statement is very important, because if no mistakes are made then no problem solving is taking place. We need to never ridicule nor allow other students to make fun of their peers for making mistakes. We need to let them know their mistakes are imperative to everyone else's learning. Rose and Gabe, what do you think about making mistakes? What do you see in your placement's that either enforce or go against what we've read and learned about making mistakes?

Week 4 Math

Within the articles we read, they discussed accommodating all students in different mathematical activities, by giving problems with many different solutions and teach the many different approaches on how to solve a problem. This helps the less talented students participate in the same task with the high talented students. Teachers are able to support high achievers, and also accommodate students who are a bit behind. The lesson plan is incorporating all talents. Open ended answers are great examples because students can write their responses to the story problems on however they solved it. There are many different ways of solving a problem, and it’s their preference, and what they feel comfortable with. They will still have confidence with themselves if they were able to get the same answer as the other high achieving students in their math class. Maybe once they are more comfortable with the problem they will be able to learn and observe their peers’ solutions.

I enjoyed the actual examples of the different solutions different students came up with. They all came up with the same answer, but getting there was different amongst their preferences. If they are taking the problem and solving it in their own way, you know that they are grasping the concept since they made it their own way of solving it. I noticed a pair of students working on an algebra problem in a picture, and I believe partners in assignments with this approach of open ended questions is wonderful because they can learn off each others’ solutions.

I liked the open ended form example in the Kabiri & Smith article. It asked the student to draw two different congruent right triangles. There are many different triangle shapes that contain these traits, so allowing them to draw their own helps those to understand the concept better. Open ended question makes the problems more authentic and meaningful to the students.

In my placement, I do not see any of these open ended questions and discussions in the math portion. She gives a lecture, allows questions, but they are not working together solving it in different ways. There are yes and no questions, and only one way to solve the problem. They work on worksheets and do a lot of fill in the blanks. It seems that majority of the students do a good job answering these worksheets, but I can tell that many of the students are so bored. This is not good that they are already bored with the repetitive questions at such a young age! This could be changed by giving fun story problems (maybe some that even use their names), more open ended questions, and group discussions or math activities. I believe my CT does do a good job accommodating all of the students, but I am sure she would be interested in reading these articles on ideas on accommodating the students that are struggling.