March Journal Summary #2

The second article that I reviewed was found in the Mathematics Teaching in the Middle School and was titled The Value of Guess and Check. The author states that guessing and checking encourages the development of problem-solving skills by forcing students to try and make sense of the material involved. Having the students gain a better understanding of quantitative relationship is also one of the main goals shown throughout the article. Word problems can never be underestimated while students are learning new concepts. By giving the students the opportunity to guess and check helps them look deeper into the problem and eventually understand it more. Eventually, the goal is to have the students not go through the process of guessing and checking each time a problem comes about, instead they will know how to go about the problem faster and more efficiently. This will not only help the students learn more material in a shorter amount of time, but will give the teacher more time to look at and help students in problem areas. “Guess and check is a powerful problem-solving strategy that can connect a conceptual understanding of word problems with a symbolic representation” (Guerrero, 398).

The value of guessing and checking has always been important to me. Through my educational career I made use of the guess and check method on many occasions. I have learned that by guessing and checking I look deeper into a problem and it helps me understand it more fully. This is an aspect that I would like to incorporate in my own classroom someday. The more a student looks into a problem, whether it is a number problem or a word problem, will be better for them in the end. Hopefully, as my students travel through their academic careers they won’t have to guess and check as much as they did when they first started out. My reasoning behind this is that they understand how to go about a problem quicker and more efficiently. There is a strong possibility that this method will be incorporated in my teaching atmosphere in the future.

Guerrero, S. M. (2010). The Value of Guess and Check. Mathematics Teaching in the Middle School. Volume 15, Issue 7, (392-398).

http://www.nctm.org/eresources/view_media.asp?article_id=9176

March Journal Summary #1

The first article I reviewed was found in the Teaching Children Mathematics journal and was titled Identifying Logical Necessity. Teachers are used as facilitators throughout the article expressing the importance to make wise reasoning when describing things that happen. The author goes on to state that teachers that know more about the topic regarding logical reasoning are more prone to be able to help elementary students understand the concept. Logical reasoning should not be taught explicitly in throughout a students elementary years, but should instead be presented when an instance occurs that could be related with the topic. Activities used throughout a student's day to day learning should incorporate and encourage students to explain their ideas by reasoning with proof. Proof is vital for a student to grasp onto early in their academic careers since the term is at the root of explaining reasoning and proof. Determining where a student is struggling with their proof statements is something that all educators should master. Mastering this skill will help guide young students throughout K-8 and will prepare them for the next step in the educational careers.

A teacher’s main goal is for their students to learn the material being taught and to have them succeed as they go through their academic endeavors. Students that are able to recognize and explain their reasoning and proof methods will do well as they move on. Teachers must make it one of their main goals to make sure that they are able to recognize and correct a student that is struggling in their logical reasoning. The article expresses numerous activities that will help teachers sharpen their skills in this area and is a great resource that I can see myself looking back to in the future.

http://my.nctm.org/eresources/view_media.asp?article_id=9162

Video work #2

The second video work was done for the grade level of seven and focused on “lessons and graphs.” The teacher explains that she made multiple graphs showing different things. The students broke off into groups of their own making and were given a copy of the graph. She wanted the students to be able to come up with their own pattern of the graph in table form and to come up with the remaining values from those that were already existing in the table.

1. Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.

By having the students coming up with their own stories they are able to look at the material in a more personal level. This will hopefully help the students bring more personal interest in the material along with them putting more passion and pride into their work. Taking this information and building it around math hopefully will help the students bring about more understanding of why the connections relate to one another.

2. Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.

The students could have each come up with more than one story and related them to one another. This way they would have had more experience in the comparing and contrasting aspect. Representation could have been used more too which could have been used in ways like building things actively or using the students to build a life-like graph.

3. What criteria do you use to determine whether or not to use a particular task with your class?

I am novice teaching right now in a 7th grade social studies class so I can relate well to this topic. Every time I am about to do a lesson I try to think of ways to connect with my students on a personal level. Also, knowing what my students enjoy learning about could prove to be very useful. This aspect of my teaching will come with time as I learn more about my students as I am around them day in and day out.

The overall use of the video was helpful as it gave a real life example of good teaching. There are numerous things that I could see myself making use of in the future as I go through my teaching career. The movies showed a little light on the things that I could better myself at and hopefully in time I will be able to master quality learning techniques.

Math Applet Blog: 3 - 5

The math applet that I chose for the grade level third through five included: Communicating about Mathematics Using Games: Playing Fraction Track. This applet involved the use of fractions and the student’s ability to understand how the fraction chart was built. The chart was built in a way where the smaller of the fractions was located on the left while the greatest was on the right. This was done so in a pyramid manner and would have to be discussed and understood by the students before the game began. The ease of use for this applet would be tough for a student that was not familiar with how the fractions compared to one another. This activity would help the student’s progress to a higher learning of mathematics once they figured out the concepts. The students would be assessed by their ability to play the game/activity to the best of their abilities while trying to learn the concepts fully. Students that are having troubles understanding the material should be placed with another student that understands the material, but could explain it in a way that the struggling student would be able to comprehend. The only concerns I have with this applet is that it could prove to be tough for multiple students and eventually hold some students back from moving on to the harder material.

http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm

Math Applet Blog: Pre K-2

The math applet that I chose for the Pre K – 2 grade level included: Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams: Tangram Puzzles. The main objectives for this applet included the ability to describe figures, along with the ability to see the formation made when the shapes are changed through the buttons located in the applet. The applet has the student use different shapes to fill in an outlined image. This type of task should be very simple for the students to understand and something that they could do on their own without much instruction. The students will have a better understanding of geometry when the time comes because of the background that they received with these different shapes. The teacher can create student discussions by asking them certain questions pertaining to the applet functions. A good example of this would be, “what happens to the shape when you flip it?”. An easy way to assess the students would be to see if they were able to identify and use all of the shapes to fill in their respective outlines. All in all, this is a good applet for the younger students and is a good stepping stone that will eventually lead to higher learning.

http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm

MTMS Article Summary

Mathematics Teaching in the Middle School recently published an article title Calculus in the Middle School?. The main idea of the article is to express to students in the middle school that they can in fact further their understanding of higher education math. Students who have a background in the content area and information pertaining to calculus are found to be more eager and willing to go further in mathematics. The authors of the article also state that there needs to be a change in the way that calculus is perceived among young students. Introducing topics that can be related to higher level math could get the students ready to dive into harder and more advanced math later in their education careers.

This information would be very helpful to me since I want to teach students in late elementary. I could help the students get ready for what they are going to encounter in both the middle school and high school. Getting students eager and excited to learn about higher levels of mathematics could help them in the long run as they travel through their educational endeavors. The article has some good ideas in it, but overall didn’t really jump out at me. I am more so a social studies guy, but the information and ideas expressed are things that I can see myself making use of in the future when teaching.

TCM Article Summary

The article titled Transitions from Elementary to Middle School Math posted in the TCM journal expressed the need that teachers need to recognize and help students as they make the transition into the middle school/junior high. Students come across changes made with regards to how the aid materials are presented to them and the difficulty level of the material. It would be best for teachers at this level be aware of all of the challenges and difficulties that a student may run into as they make the transition. By doing this the teachers will be better at preparing the students to leap frog the challenges. The authors also talked about the involvement that the teaching community must have with one another. Having middle school teachers make visits to the elementary schools and having direct communication with the staff could help them understand better ways to help students who are making the grade level transition. Elementary school teachers must also be familiar with what the students will encounter at the junior high level. It would be best for the students to have the opportunity to practice learning at a more advanced level prior to making the transition. Connections will be vital for the students to make and act upon when they are preparing for junior high instruction. If they are familiar with the methods then they will be able to learn to their full potential without having declines in academic achievement. More importantly, the students will be ready to learn and build upon the concepts and knowledge they already have pertaining to mathematics.

This would be very helpful as the students would be very familiar with what will be expected of them in at the junior high level. By having teachers that are prepared to help guide students through their transitions into the upper grade levels then they will have a greater possibility of success. The article stated many good points that I can see myself implementing in my classroom, but the main concept of preparing students for their transition really hit me at home. As a teacher I will want to see my students go on to do great things so it is important to myself that I do all I can to help the students grow.