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.

New Insights & Theri 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?

Mathematics has never been an easy subject for myself. Since this class has started I have taken a different outlook on mathematics. I have learned that there are many ways to arrive at an answer and that each way is beneficial to the learner, if she/he can give an explanation at how they arrived at the answer. I have learned that some of the reasons I fear mathematics is because of the way I was taught at an early age. Having a math teacher who is good at his/her job is so important because in mathematics one concept builds upon others and if you are not understanding a concept you may need the additional help from the teacher. I remember there were times when I was in junior high and the teacher didn't get as far as he/she had hoped and that teacher would blow through the material like it was nothing. It was brutal and I didn't like it all. I felt like my learning was suffering because I didn't have the time to practice the material and the material was not presented in a learn able manner for me. I was a visual and hands on learner. When it came to math I needed lots of practice. I was accountable for learning the material if I didn't understand it. I would occasionally go in for help, but this did not work at all times. I believe this is where I started to fear mathematics. I knew later down the line, math would become harder and that there was nothing I could do, but relearn concepts from earlier years. This scared me. Integrating mathematics into a classroom is very important. Students need lots of hands on learning and ways to make the material relevant to their own life. The teacher needs to differentiate his/her instruction to meet all the needs that exist within a classroom. Mathematics can be fun and less intimidating if the teacher is good at her/her profession and allows for his/her students to learn alternative routes to an answer. Problem solving on your own can be very effective in learning how to think on your own and solve on your own. Math takes time and lots of practice.

New Insights and Their Implications

I had originally thought that there was only one way to teach mathematics, by giving formulas and showing students how to work through them. That was the way that I was taught by almost every math teacher I had from K-12 and into college. After starting this course, I now see that there are more sophisticated ways of teaching mathematics to students. We have learned in all of our education courses that children learn best through hands-on experiences and when they are given some ownership over their own learning. These learning theories have been long-standing foundations in the education field, so why are we so hesitant to give students ownership of their learning in mathematics? I think many teachers are afraid of the loss of control and the increased effort in planning it takes to allow a completely student-centered classroom. The implications of this new insight are that I am going to have to put in a lot more effort when designing my math lessons, but the benefits for my students will far outweigh the effort. If I can apply the concepts we have learned thus far and challenge my students to be problem solvers and creative thinkers, I will spend a lot less time covering the basics and reviewing and be able to take my students' level of thinking higher.

New Insights and thier Implications

Since the start of this class I have learned many new things that deal with the national and state standards and how we should be teaching math. I feel that it is really important for us as students to learn everything we can about the standards becuase if we do then we will have the knowledge to teach our future students to the best of our ability. Also I learned how helpful the state standards are. I never knew that there was a place where teachers could go and get resources for lessons. It will be helpful for me to refer to when I become a teacher. The second thing that I have learned since the start of this class is how we should be teaching math. Teachers today should cover fewer topics so they can spend more time on each subject to ensure the students really understand what they are learning. Teachers today are required to cover so many topics that the teachers do not have the time to have good discussions about the material to make sure all the students understand the topic. By teaching this way it only hurts our students in the long run. Teachers need to make it so students have to think outside the box to come up with answers and the teachers should provide opprotunities for students to arrive at answers in multiple ways. I feel that if teachers give the new way of teaching a try they will like it a lot more and they will find that the students will have more fun learning. As of right now I have gained a lot of knowledge on how I can become a better teacher and I look forward to learning more in this class.

New Insights and Their Implications

These first couple weeks of class, I have learned a lot of new concepts not only about math, but education overall. I knew this math class was going to be different than any other math class I have ever taken and I’m glad it is. I struggled through every math class I have ever taken besides Geometry in High School. I feel intrigued about this new way of teaching math, teaching the mathematical process of thinking and problem understanding rather than focusing on the solution. I am excited to learn more about it so that I may teach my students from a new perspective.
The last few days of class have been focused on standards and their interpretations. Past classes have talked about standards and having to align our curriculum to the standards, but the standards have never been broken down and explained in the way they were in our class. After our class discussions I have realized how important it is to understand the meaning of them, and how important it is for teachers to be involved in the revision process of the standards. We as teachers cannot rely on just state or NCTM standards, a connection between all are needed to be a quality teacher in any content. Looking at the Curriculum Focal Point document and the unpacking language at our state site will better translate and define our standards.

New Insights and their Implications

With talking about standards I have learned many new concepts about and how they can affect me as a teacher. I have discovered that it is important to know and understand all of them before you can properly teach them or the content in them. I did not know that the teachers of south dakota were the ones responsible for the construction and fine tuning of the state standards. Standards are an important resource as a teacher because not only do we need to teach to the level of the state, but also to the standards of the nation. I do like how the national standards are more clear when they are talking about the material. Other concepts that I have learned about so far are how to teach in a different way that I was raised on. I dont know if it is helpful or not yet simple because it worked for me so I dont see anything wrong with it.

I think the new method of teaching math sounds like a promising idea. It is more important to make sure the students understand math as a process and not just as a rule or drill that you do the same way everytime and get a final answer. Having mulltiple ways of doing something allows children to explore and have fun with problem solving. By encouraging them to try different methods they are actively engaged in the problem solving process. Personally math has never been fun for me because I have just simply never been good at it. I dont blame anyone for my failures in math but I do wonder if maybe I was taught differently I would like math better and be better at it. Understanding the underlying concepts about math is much more important than getting the right answer.
In these first few weeks of class I also found out a lot about the standards and how they work. It is interesting to know that the South Dakota standards do not always line up with the national standards and the NCTM standards. I always thought that they were aligned after each other. I think that being apart of creating the standards is something that I would be interested in doing when I get out into the teaching field.

New Insights and their Implications

In the first couple weeks of math class I have learned some new techniques I can use in the future to teach math. We have discussed how it is important to build confidence in our students so they will believe in their own math skills. As teachers it is also very important to access their students’ prior knowledge and build on that.

I also have obtained a lot of new resources that I can use when I am writing lesson plans to include important information that I feel the students should know while aligning the activities to the state and national standards. One of the resources that I found particularly useful was on the state standards website, I was previously unaware of the assessment section as well as being able to access sample lesson plans that explicitly aligns with the standards. I am sure that I will be using these sections to give me ideas about lessons that I can teach as well as be able to focus on the sections that the students will be tested on when taking the standardized tests.

New Insights and Their Implications

I have learned many new concepts about teaching standards, where they have come from, and how they can affect me as a future teacher. The new concepts that I have learned about teaching standards is that it is important to know and understand all of them before you can properly teach them or the content in them. I have learned that our state standards come from the teachers in South Dakota and that they do not always aligne to the national or NCTM standards. For me, this is an important topic because I think that it is much more important to aligne the state standards to the NCTM standards. These standards have more of a clear focus and cover the material that needs to be covered in more depth. Other concepts that I have learned about so far are how to teach in a different method such as helping the students get to the right answer and not just stating the answer that they need to pass a test. This method will help my future students learn the concepts in math and help to retain them longer then if they were handed the information.

New Insights and their Implications

Within these first couple weeks of math class, I have obtained much important information pertaining to the teaching of math. The first area that I have gained much insight into is the teaching methods of mathematics. I have always been used to "drill and practice". In other words, many of my elementary and high school memories of math class consisted of here's the formula, here's how you do it, and here is your assignment. However, as I have learned from reading chapter four and classroom discussion, this method is not benefiting our students. The graphs presented on the first day of class really helped me to gain an understanding for this information. It seemed as though we were doing everything wrong in relation to the countries that were showing success in the area of math. These statistics implicate that we need to go about teaching mathematics in a more beneficial way to our student I am slowly developing an understanding for the teaching methods being presented in this class both from the reading, and the group assignment we have just completed. I am eager to learn more.

The second area of study in which I have gained much insight into revolves around the state and national standards. When we first began talking about these standards I was somewhat overwhelmed. However, through class discussion I was able to develop an understanding for the reasoning behind involving the national standards into the math cirriculum, and the importance behind them. As we have learned, the state standards are somewhat broad, giving us no area to pinpoint our lessons. However, by referencing the national standards and the focal points, we are provided with more direction into what our students should be studying.

New Insights and Their Implications

I have been learning a lot about state and national standards. In all the classes before this we have had to write lesson plans with standards, but these standards have never really been explained. I knew that they were to help teachers make sure they were on the right track with what they were teaching thier students. This is the first time where I have had to go through the standards and be able to understand what the standard want and what they mean. Also I have learned where to go online to find information about standards if I do not understand what they mean or to just make sure I am understanding them right. I also like working with my peers, when we are going over standards, because that helps me understand what we are suppose to do or get something that I missed.

New Insights and Their Implications

I would say the newest insight that I have received from this class is the knowledge on standards. I have learned about how the state standards are created, I have actually now seen the national standards I have never seen these before, I have learned of the importance of alignment with these standards in my future classroom, and I have learned how to better navigate around South Dakota State standards website.
First, learning about the process of reviewing the state standards and then every 5 years making changes to them was new knowledge for me. Second and third I will put together, sadly this is the first time I have actually seen the national mathematical standards. It was very interesting to me how they are very different than the State standards in wording and how the state standards have left some of the national standards out. By me now knowing how to get access to both standards, in my future classroom I will be able to better align my classroom curriculum. Not only meeting state standards but taking a look at the national standards and finding ways to better educate my children to a larger scale. Finally, I have been to the South Dakota State standards website many times, but I never knew of all the different things I could do there. Like accessing the blue print to the Dakota Step, and ways to unpack the standards to get a better understanding of what is expected.
Everything we have covered so far in this class I see as being something that is going to be very important to my career as a teacher. Even if we have been running out of time and not covering all the material Dr. Reins wants to. I am glad that we have gone into a lot of detail over most of this material, and not just brushing it leaving me with the sense of not gaining any knowledge.

New Insights and Implications

The insight I received from the lesson on standards, was that it has helped me to see that the task of aligning could be very complex, but it is matter of looking at the big picture and finding the focus of the standard. There are many resources out there to help you to align and understand the language, the purpose, or how it will be tested. When you utilize your resources it will only enhance your teaching and benefit your students. I also was able to see how the whole system of standards really works together and how it is tested within the schools.

When applying this to the classroom situation, teachers should always be reevaluating their teaching and activities for accountability purposes. Regardless of the situation, it is important to stay on top of your curriculum and evaluate it from every aspect and ask yourself how could I make it better even if it went smoothly. If you truly care about your students and their learning you should want to give them the absolute best learning experience; good instruction should align to the standards and prepare students for content on state and national tests.

New Insights and Their Implications

I have learned many things over the first couple of weeks of class. I first thing that I learned is that we need to start teaching math to our students in different ways. We cannot just give our students the answers and expect them to memorize everything. We have to allow our students to problem solve and find solutions on their own. By doing this, the students will better be able to retain the information that is being taught to them. It is good to have a student-centered classroom and allow the students to have hands on experience and be part of the discussion in class.
The next thing that I learned from the first couple weeks of class was how to read and interpret the South Dakota Standards. We have to align our lesson plans with the SD standards in every subject. That use to be the part I hated about writing lesson plans. I could never find a SD standard that matched my lesson well enough. It is good to know that there are the NCTM expectations and the focal points that are available to that you are better able to interpret the SD standards for the subject of math.