Week 15 blog posting

I read the Barody and Bartel article. I picked this one because I thought that the idea of connections was interesting and something worth discussing. The author makes a very clear argument in the first section of the article. He states that "Research suggests that understanding can be viewed as a connection between two pieces of information (Ginsburg 1977), and an understanding of elementary concepts is essential for mathematical power, for example, applying school mathematics to everyday tasks, inventing mathematical procedures, understanding and solving genuine problems, and comprehending more advanced mathematical ideas." This sentence totally convinced me of his idea and drew me to want to read more. The author then goes on to talk about the use of concept maps to achieve this goal. While this was something that I had never thought of before, the author makes sense. That using this model allows students to draw their own connections on the concepts of math. This will also give information to the teacher about what connections the students are making versus those that we want them to make. As well as showing students how everything that they learn builds upon itself and is all interconnected. I believe that this is an interesting way to show students a new technique and grasp their knowledge.

Week 14 post

To our group: I am very sorry this post is late. There was quite a bit of confusion on my own part of whether we had to post or not this week.

When it comes to how the equal sign article relates to the activity that we did in class, I feel that it can be very confusing for children at an early grade level when it comes down to it. As we figured out from 2 weeks ago, the equal sign can cause many many confusions when looking at the way that students write it. Having students express the equals sign as "the same as" instead of "equals" causes many confusions as well. As we saw in our class it comes with a lot of debate about what and how it should be used. I feel that we need to make a standard for not only our classrooms but for how our students can best understand it. The equals sign is obviously a very basic thing that is used in mathematics everyday. I think that if we don't get a good basis down for our students at an early age of appropriate ways to use it then a lot of debate will still come about, just like in our classroom.

Week 12 Post

I really enjoyed reading the Whitenack and Yackel piece. I believe that it simply presented a lot of good information that could be really useful to us. In my experience it is rare for students to challenge one another by asking questions about their process, although I believe that if this were happening more it would only benefit the children more. In the scene on the second page where Casey's logic is challenged by Teri, it allows us to see the very clear distinction between people who are looking for explanation versus those who are looking for a justification. Students who are looking for an explanation do not understand the problem, while those who are searching for justification believe that they know the answer and that the one they are questioning is incorrect. This distinction is key to understanding when teaching math because it will allow you to properly answer the questions that the students are asking. The article also states that this discussion is a learning opportunity for all students because it will help them develop the ability to form mathematical arguments and will in turn advance their mathematical thinking. This is something that every educator should want for their students, and through methods such as these, I believe that it is possible.

Week 11

The Smith, Bill, and Hughes article reminded me of one we read towards the beginning of the semester called Mathematical Tasks by Smith and Stein. This article was about creating open ended tasks that use a high level of thinking. Mathematical Tasks emphasizes the importance of task choice and the type of thinking that a certain task invokes. It is very important to know what you want students to get out of a lesson before implementing it. More so, tasks need to be set up in a way that encourages a high level of thinking and involvement in the task. Thinking Through a Lesson also discusses this but relates it to collaborative planning, much like we are doing for our math lessons. When discussing collaborative lesson planning, the article points out that teachers can better anticipate student responses and can generate questions that will promote student learning before actually teaching the lesson. Having input from 4 teachers is certainly more helpful than just your own.

The list of questions from Developing Mathematical Thinking from Effective Questions, will be very helpful for our lesson study planning. Thinking of these questions before teaching the lesson will be important in order to gage how students will be responding throughout the lesson, and guide what we would like them to take from the lesson.

week 10 post

When I first saw the articles that we were to be reading this week, I was intrigued by the article titled " 10 Practical Tips for Making Fractions Come Alive and Make Sense." This is something that I, as well as my students, could definitely benefit from.  I thought that the first point was very useful. Focusing a lot of time on the actual idea of fractions is something that I believe will help children. They need to have in depth understanding of what a fraction is and how it relates to a whole in order to be able to relate it to manipulatives and word problems. Another tip that I found to be very useful was #3 which stated the importance of fractions as being numbers. Children understand numbers and therefore if they understand fractions as such, not as a foreign idea, they feel that they are more tangible. The author suggests that you should do this by using number lines and other such tools. I wish, and believe that my colleagues will feel the same way, that we had more articles like this because it was so useful. The article actually gave things that we could do now and later in our classrooms. Thanks for the information Nic!

Week 9 Post

The first thing that stood out to me in the Wearne and Kouba article was that they admit something that everyone knows is very true, that students have lots of trouble with fractions and proportions in general. At the same time we also know that these tools are very much so needed for students as they progress through both school and life. I found the sample question of "How many fourths make a whole?" to be interesting for many reasons. One is that the only 50% of fourth graders answered the question correctly and 16% omitted the questions all together. The fact that almost 1/5 of the students omitted the question is scary to me because that means that they did not even know where to begin to find the answer, let alone what it actually was. When in actuality the answer was right in front of them! I hope that my students will test better than all of the sample results that we see, because the results are not where I want out youth to be mathematically.

I believe that manipulatives can be very helpful to students when they are learning proportions and fractions. This is because they can visualize a part of something when they can see it in front of them. Seeing 4 of 10 pieces slices is tangible and makes it more sense to many students. the part that I need help with, and many students need help with is the transferring from visual aids to mental math. Students have trouble making this jump. Does anyone else have ideas as to how we can help our students with this problem?

Week 8 Post

So it's been awhile since we all met for this class, and I would like to pose a question to my group about 2 different activities that we've been doing compared to the readings that we did. I recently was able to do my student interview in class and found that the different levels of understanding addition and subtraction concepts really vary throughout my classroom. I used Fact Triangles for my interview and had my students use their addition and subtraction facts to hopefully realize how 3 different numbers will correlate back and forth between the properties. I interviewed 3 different students in the class and feel that only one was able to clearly grasp onto these concepts. I was wondering what lesson was done for each other members interview and how their results went. Was it something you expected? Did it surprise you in any way with how your students responded to your questions? The second activity that wasn't mandatory to do but something interesting was the toothpick activity. I got 3 different answers for it. Each student picked a different number and only one was correct. Were you able to do this activity with our students? What results did you get for it? I really found this activity interesting because of the results that Nic showed us in class were in direct relation to our year in school and a very low percentage were able to get the answer correct. I was almost embarrassed by the amount of people that got it wrong. We have not gotten into fractions completely in my class yet, but we have started to look at it through the use of time in my class. How are fractions brought up in your classes? Do your students enjoy them? I know I always liked using fractions because I was able to use them at home and help work with my dad on things. It was able to hit home for me and something I ultimately enjoyed doing. Some people completely hate them though. How do you feel about fractions? Now I know I asked a lot of questions during this post, but I think we don't always have enough time to know how each of us our doing in our classes if we don't sit at the same table. I think posing these question will also help me and hopefully help each other for our write-ups and help to see how we are all doing up to this point.

Measurment

Friends, I am so sorry I forgot to post earlier this week! I have total responsibility for the blog being posted late.

Chapter 19: Developing Measurement Concepts presented a discussion on how important the concepts of measurement are. For my New Literacies project in Language Arts, I plan to use a comic strip to present numeracy. To me, numeral literacy is how we use mathematics in the functions of our every day lives. I use concepts of measurement all the time from when I cook my breakfast in the morning to when I set my alarm at night.

I learned quite a few new ideas from reading this article, specifically the measurement instruction sequence of experiences. Many times when students are learning measurement, they do not conceptually understand what they are doing, they are simply connecting two points and counting. Students must first learn that measurement is a means of making comparisons. Next they will understand that the comparisons are made by using units that produce a number called measure. Measurements are made by using a common unit to make the comparison. I also learned that nonstandard units make it easier to focus on the measurement and they can be motivation to students.

I like that this chapter had a lot of examples and activities. They will be useful for reference when I am teaching measurement in my classroom.

Week 6 Post

I found the article on lesson study to be extremely interesting and relevant to our class right now. There was a lot of dislike when the math lesson was assigned and I believe that lesson study and the lay out of that project are similar. In my eyes, watching someone teach is extremely useful, especially when we will spend so much time next year running the lessons and classroom on our own. Also the idea that it is led by other teachers is very useful. Teachers often look at researchers or educators as being out of touch with the classroom. This means that they often do not believe that what they are teaching them is feasible in their classrooms. If this is led by a fellow faculty member, someone they know well and respect, it could have a huge benefit. The teachers may believe in the idea or process more and see how it can be implemented into their classroom. I know that I feel more comfortable when discussing something with my peers than with an authority figure. This most likely is also true for most teachers, since we are almost them :). I liked the way that everyone being involved in the planning is stressed. That might be a problem that American teachers see with this plan is that their ideas and processes will not be a part of the lesson, and they don’t like that. But, I believe that by stating u front that everyone’s ideas are important and everything will be decided together will help put some teachers at ease with the entire situation.

Week 5 Post

After going over the readings for this week, I was able to compare man things from them to the classroom that I work in. From the “Student Mistakes” article I was able to draw many similarities from the kindergarten classroom to the first grade classroom that I’m in. One of the first things I saw was the use of the calendar and how the students use counting techniques. One aspect of the calendar that I really like about how my CT uses it, is that she has the students tell the next numbers for the calendar and then has each number with a different color and pattern on it. The students then get to guess the pattern and need to get the correct number, pattern, and color for the number to go up. Following the calendar technique, I’ve also noticed that my first graders sometimes show signs of how the kindergartners would say “60” as a “5 and a 9” then a “5 and a 10”. When something like this does happen, usually the student picks up the mistake or has help from the other students in the classroom. Another common mistake that the article showed was students seeing numbers like 730 as 70+30+0. I have seen many mistakes like this in my class when comparing larger numbers. For some reason place value in the hundreds place is difficult for them. Place value is a very important aspect to math learning and something I feel that needs to be drilled into students at a young age so they can get a really solid grasp on it.

Week 4

I am glad to have read the Smith and Stein article, as I know have a set of guidelines to check the level of thinking involved with a given problem. This article highlighted the importance of task selection. It made me more aware that there are different levels of thinking involved with different types of questions. However after reading the article I still have a few questions. The concluding paragraph of the article says, “in this article we shared our findings concerning the importance of beginning with a task that has the potential to engage students at a high level…” I wonder what they mean by beginning? The beginning of a class period? Homework assignment? Unit? Lesson? The answer is probably all of the above. But then I ask, when are low-level thinking questions relevant?

In the Kabiri and Smith article I learned how important it is to base instruction of problems with different solution approaches and many levels of the solution. It promotes higher-level thinking for the whole class and an equal opportunity for all students to succeed. It was very helpful to see examples of how to turn a traditional problem into an open-ended problem. Specifically, the algebra problem reminded me an assignment that I was given in my high school algebra class. Each student was assigned five numbers, for example 5, 5, 3, 6, 7, and was asked to use any combination of operations and parentheses to compute the numbers 0-100. The problem was open ended and allowed students to be creative with a multitude of solutions. I specifically remember feeling extremely proud of myself at the end of the assignment.

Week 3 Post

I thought that the original idea of having a school where some of the students were taught in English and some of them were taught in bilingual classrooms was interesting. I was very curious about what all was surrounding the circumstances. How were the students selected to be in the different classes? Was there a test? Was it this way for all of the subjects? How proficient were the teachers who were teaching in Spanish and English at both languages? This may be part of my over reactive brain and my need to ask a lot of questions, but I found them all to be valid.
A second part that I found to be interesting was the section where they described the different cognitive functions that the students would need to be able to answer a seemingly simple math question. It also listed the questions that would be asked as means of scaffolding to assess what parts of the question that the student did not understand. This was something that I had never thought about before, asking specific questions to understand what part of the problem that the child does not understand. I hope that one day I will be able to have the same understanding of what I am teaching so that  I can help my students in the same way.

First Post

One of the big ideas that I noticed while reading the article on classroom diversity would be how I agree that as a future educator, we need to figure out ways to incorporate the working and middle-class students’ situations more into our teaching. The author of the article, Rosebery, went into a good amount of detail explaining different forms of teaching trends that were used to incorporate these ideas. One of the ideas that seemed to be helpful was when the teacher allowed for the students to bring in ideas based of their own funds of knowledge for discussion. Having the students engage the work on a more personal level to what situation they are more familiar with seemed to be something that the enjoyed and could relate to more. Vygotsky understood and preached that social and cognitive skills were needed when to have good learning happen. When a student cannot familiarize with the work that has been presented to them, it really causes gaps in learning. I feel that this article is trying to give us an idea that we need to focus on creating examples for our class that will relate to not just the middle class students, which seems to be the case that happens now. We are going to have to present ideas to students that might have disabilities, low income, different cultures, and different social backgrounds. If we do not engage different aspects of sociocultural perspectives to our learning, then we will not be a diverse teacher and will gap some students in our classroom.