Summary and Synthesis

I was really confused on what we were doing and how we were doing everything since the last time I blogged. I felt that we did not cover the material we were going over in much depth and I was not getting what I was suppose to be getting out of class. The mid-term exam then kind of snuck up on me and I did not know for sure what to expect from it. I remembered talking about a lot of the things that was mentioned on the review guide, I just did not know for sure what Dr. Reins was expecting. Since the last time I blogged and now that the mid-term is over, I really have a better understanding of how this kind of teaching has an impact on somebody and how we need to relate this kind of teaching when we teach. I know how to have students problem solve, think critically, and remember the information that I teach them. If they do not remember the information that I teach them ten years down the road, such as equations, they will know how to come up with the equation on their own. I am gaining a better perspective of this class and now I do believe I am getting what I am suppose to get out of this class.

New Insights and Their Implications

I thoroughly enjoyed the instructors way of teaching how to find the area of polygons. At first I didn't understand what was going on but looking back I understand what he was trying to do. It was a great way to show us how to teach a topic so students actually understand what they are actually doing. I had to look up the the Picks -Therum. I needed to see it to understand. I am not one of thoes people that can pick up a math concept without being shown how to do it. I understand it better now but I needed to see what I was to be doing. Implications include a better understanding of how to teach concepts about math so students understand what and why things work. I can teach in this style with some small changes for the different ways students learn.

Summary and Synthesis

I have learned a lot from math methods, since we started this course. The newest topic I learned about was fractions. I never knew how I missed out on when I was kid. I thought all kids learned fractions the same way, but by learning them in a way of halves and that's it, it doesn't help them in the end. Teachers need to help students construct the idea of fractional parts of the whole and equal-sized portions or fair shares. By teaching these two concepts first students will gain a better understanding of fractions. To teach these two concepts teachers should begin with sharing tasks when developing lessons about fractions. These are just a couple of the things that I have learned so far. In class we were also talking about 6 important steps that we need to know. In class we did not get through all six, but I am looking forward to learning more about fractions. Another things that I have learned from the lesson this week was how many magazines there are for teacher to get resources to help teach concepts such as fractions. In the magazines there are so many manipulatives that teachers can buy to help students better understand the concept of fractions. I am glad we were able to keep the magazines we received in class because it will be a good resource for me when I become a teacher. Fractions is a tough topic to understand for some students, but with the right help from teachers and from the the use of manipulatives learning fractions can be fun.

Summary and Synthesis

Sitting in the first day of K-8 Math Methods, I felt somewhat apprehensive. Math makes me nervous. I have never felt confident in math. When we received our first math assignment, I was nothing but nervous. To be honest, I was not accustomed to this type of problem solving. I was expecting the formula and process method of learning. However, I soon began to open up to this new form of mathematical teaching. The experience of different activities within our class periods have helped me to gain an understanding for the hands on approach to solving mathematics we have been learning about. One specific learning activity that has stood out in my mind deals with finding the areas of a polygon. Experimenting with different methods of finding an area of a polygon helped to open my mind to a more constructivist approach to learning mathematics. I realized the importance of exploration in mathematics, and the impact is has on students learning. Another learning experience that has impacted my understanding for exploration in mathematics would be the combing of formulas to find the areas of a trapezoid or a parallelogram. These experiences have also helped me to understand the concepts behind the processes of mathematical inquiry. My understanding for these mathematical problems stand out for one reason, because I now understand the relational concept behind the process. Overall, I have realized the importance behind helping to students to develop conceptual understanding in regards to problem solving. Many of the discussions that have taken place within our class periods have helped me to become more confident in providing a more hands on learning experience for my future students.

Summary & Synthesis

Math Methods has been an eye opening experience for me. Learning math was a hard concept and subject to learn. I have always had a somewhat negative attitude towards math, because it has been a trying subject. Since taking Math Methods I have learned a different way to approach a problem and learned the strategies to solving a problem. I have also learned that the way I was taught was more less repitition and learning the information for a test and less learning on how to discover strategies and patterns to problems. In Math Methods I have learned that students need to be able to have a solving strategy that they can justify and have multiple routes to explore for an answer. I like the alignment process. This alignment component provides a continious loop of modifications and improvement of learning and teaching.

New Insights and Their Implications

It was interesting learning about the different steps you have to teach in order for students to be able to learn fractions. There are some things that we talked about in class that I never really thought about when working with fractions. Fractions was one concept that I thought was very difficult to learn when I was in the younger elementary grades, so that is why I found this to be so insightful. Talking about this in class gave me a new perspective on how to teach fractions and also made me realize the different new terms that you need to introduce to students when learning about fractions. I also thought that looking through the magazines was very helpful to get some ideas on some hands on activities that you could use in your classroom. Learning about this was very helpful for my future teaching of fractions and ratios.

Summary and Synthesis

Before thursdays' discussion on fractional concepts I thought of a fraction as a number over a number, the top being the numerator and the bottom number the denominator. A fraction simply tells us what part of a whole. After discussing fractional concepts in class, I see now why I, and many students sturggle with fractions; its because we lack the foundational understanding of fractions. There is so much more to fractions that I was never taught. I just learned the basics. Thrusdays discussion on fractional concepts gave me a whole new perspective and knolwedge of fractions, for my own persoanl understanding, but also what I need to do as a teacher to help students understand concepts of fractions. I am now aware of the 6 steps that need to be followed/taught for the development of fraction concepts. In class we discussed the first 3 steps. Step 1: Introduce Sharing and The concept of Fractional Parts and Understanding of the Unit, we discussed students notion of fair sharing and the teacher's job to break students away from using a halving strategy. I learned the best way to do this is to change the number of things being shared and the number of sharers (odd division) to force students to confront their halving strategies. Students must also understand a "unit" of a fraction before they can compare parts of a fraction to a whole. Step 2: Introduce Models for Teaching Fraction. During class we looked through two different magazines that had a wide variety of different models/manipulatives for students to use to help them understand fractional concepts. Choosing what manipulatives to use is very important for teachers to consider. It was brought to my attention, that what we see isnt always what the student sees. Therefore, we must choose manipulatives properly, introduce them to the students and ensure they will enhance and assist students learning. I also learned from class discussion that the lables on the models can sometimes take away from students true understanding by dening them the oppprtuinity to reflect on the size of the peice relative to the whol and decide for themselves what the fraction is. Lables on pieces also remove flexibility in the materials. Teachers need to consider these factors when using manipulatives. Step 3: Intrdocue Fractional Symbols. Here we discussed the importance of building ideas and notions first and then introducing symbols. In class we also determined the difference between fractions and ratios; which sadly none of us could explain the difference when asked during class. After comparing and discussing the two, we arrived at the notion that a fraction is a realtionsip between a part and a whole and a ratio is a comparision of two distinct sets. After thursdays class discussion, I have a better understanding of fractional concepts as far as the first three steps go. The topics discussed in class have helped me understand the way students learn and what specific concepts and ideas I need to teach them about fractional concepts prior to teaching them fractional computation.

Summary and Synthesis

Looking at the different magazines with all of the manipulatives really showed me how important it is to be well informed on what is needed in the classroom. There are SO MANY options to choose from that I imagine it can be quite overwhelming. Additionally, before class I would have thought that having the labels on each model would have been helpful. However, now I see that the models can be more versatile when they do not have specific labels on them. Furthermore, it has been brought to my attention that students need to be slowly introduced to certain concepts. Simply showing them the full blow concept of fractions, for example, will prevent them from actually learning about fractions. Teaching a concept slowly over a large period of time is significantly different than what I grew up with and what I had previously thought. Overall, I feel that the steps that we have learned and continue to learn about regarding developing concepts will help me to better understand how students learn and how to approach teaching a wide range of concepts.

Blog 2

Summary and Synthesis - After class today I realized how important using materials and models are within a classroom. But, it's not just important to use them if the students aren't going to get anything out of using the materials. When using a model within the classroom, it has to have a purpose that will benefit what the students are learning, and align with what the teacher is trying to accomplish within the lesson, not just do the activity or use the model because it is fun. Also, many teachers have the thinking that if the student's use the manipulative's that they will just get it, but this is not the case. A teacher must use the manipulative correctly so that it enhances the student's learning and assists it. I find this very helpful to me as I enter the profession, it makes me think more about the activities that I would have planned, manipulative's that I would use, and why it makes sense to use a certain activity. So, in summary, I find the discussion we've had in class the last couple of days very helpful in preparing me to plan lessons and the use of manipulative's.

Questions on Constructivism

How is it that constructivists know we can not know objective reality? Wouldn't one have to know objective reality to objectively know that we cannot know objective reality? (Wow, that's a lot of "objective" words). It seems to me that the underlying statement is, "We cannot know objective reality, except that we know we cannot know objective reality." (apologies if I am setting up a "straw-man"...I'm posing the statement to better clarify my question)

Constructivism

Constructivism is a reflection of our experiences and how we look at the world as a whole. As a teacher, we need to remember how each student learns individually and that instruction needs to be differenientiated to meet the needs of all students. What works for some, might not work for others, so differientated instruction needs to be part of the daily lessons. Constructivism also means we need to be able to relate what we learn to our lives. Making things relevant to our own life, makes it easier to put things into perspective and to have a handle on new material. Teachers need to create an environement where students can focus on making connections between facts. Students need to learn how to analyze, interpret and predict information into their everyday learning. Promote an environment that makes students think for themselves. Students need to be held accountable for their own work and progress and having your students participate in their own learning by thinking on their own, is the beginning of a new strategy to advance their own learning.

constructivism 2

I still believe that constructivism is a student centered approach to learning. I believe it is abut providing the students with appropriate experiences that allow them to change and add on to their existing knowledge.

Constructivism 2

After class today I still feel the same about constructivism. At SDSU we talked a lot about constructivism. It is interesting to see it applied in different ways and to have it explained in different ways.

Constructivism

After class today, some of my thoughts before about constructivism still hold. I know that it is a learning theory about knowledge and learning. Before I thought that it was more something that we taught, or part of a theory of teaching but it's not. This is a theory about how a person comes to know something. After class today, I feel more comfortable with the term constructivism but feel that it is a theory that I will need to read about and find more about before I begin teaching.

New Insights and Their Implications

New Insights and Their Implications - What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?
Math has always been a difficult subject for me and I was nervous to take this course! After being in the class for a couple of weeks, the course isn't as "scary" as I thought it would be because everything is explained really well. I have learned the importance of helping students find ways to solve their own problems and that when it comes to solving story problems, there is no right way. I'm interested to see what the new SD Math Standards will look like after they are recreated later this year. I also like that we are also incorporating the NCTM Standards- they are very easy to understand and provide lots of activities to correlate with specific points.

Constructivism

I know that constructivism is a developmental learning theory that Piaget believed in. Children are encouraged to think constructively because it helps them become more aware of their own thinking process as they are making meaning in different things they do in their lives.

New Insights and Their Implications

After the last couple days of class, I have become less scared of teaching. Having my own classroom and teaching has always been something that I want to do and am excited to do, but covering all the content and material and reaching the standards was a little daunting. But with the new knowledge of the standards and how to read them and find hints and tips on them makes me feel much more prepared to teach my students. I now know where to get ideas, right from the people who wrote the standards, for lessons about math that I can use or use as inspiration to teach my own lessons.