Week #5 Reflection

This week in our mathematics class we continued our discussion on the complexity of understanding fractions from both an educator and student perspective. As an educator it is our responsibility to ensure students are confident and comfortable when learning new concepts. We must create an inclusive learning environment where students are welcomed to ask questions and challenge their skills. In this lesson we also focused on the concept of integers and how similar to fractions they present numbers in a new, unfamiliar way for many individuals. From my own personal experience as a student the most difficult component of learning integers had to be memorizing the different rules. When educators expect students to learn through memorization they are depriving them of their ability to expand their understanding. Students retain information in a multitude of ways therefore educators should not expect uniformity in comprehension as it decreases the opportunity for individual growth. Another integral component for student success is applying concepts to realistic, everyday situations. When a connection between academic knowledge and reality is established individuals are more likely to become familiar and comfortable with what they are learning. This idea proves relevance in mathematics, especially dealing with units in fractions and integers. The video “Math Interactive” (link below) provided by our professor supports this idea. This video introduces integers in an informative manner by demonstrating how they relate to the measuring of increasing and decreasing temperatures. For students I feel a video such as this one would be beneficial as it introduces integers in a “non-threatening” manner which is fundamental when developing a base understanding. 

Through the years math continues to be given a negative connotation due to its complex nature. As a result educators must find a way to teach in both an informative and entertaining way. This can be done in a variety of ways, but for me the most influential technique to accomplish this is through games. The online game “Orbit Integers” (link below) provided by our professor is an interactive game where students go online to race against others by completing a variety of mathematical equations. This game requires fast thinking and a good understanding of adding together both positive and negative numbers. The game takes place in outer space where students take the form of a space ship. They are given a variety of equations and when they successfully complete a question they move forward towards the finish line. In the article Video Games in the Classroom Building Skills in Literacy and Numeracy (link provided below) the author prompts the idea of the incorporation of interactive video games and computer simulators in the contemporary classroom as studies have demonstrated that these outlets may be able to offer students interesting and informative context for learning. They hypothesize that the high tech graphics, sounds and motions allow participants to become active learners as they realize that their actions create a reaction allowing their level of interest to increase. The twenty first contemporary society has transformed into one dependent on technology thus educators must be willing to adapt these changes and introduce them into their classrooms to increase student success. When students feel as if they are being challenged their level of interest and motivation will likely increase therefore a game such as this one may aid in the development of individual growth and understanding of integer operations. The only negative element of the game is the nervousness which may be felt by a student when playing. It is a fast paced game which requires quick thinking and fine motor skills therefore if a student does not have a thorough understanding they may feel over whelmed. The game is fantastic as not only does it give users a challenge but it informs users of where they went wrong.

Screen shot of "Orbit Integers". Users are ranked based on the completion of the number of correct answers, as well their recorded time. As well users are shown the accuracy rate and if any questions where missed. 

Link to “Math Interactive” 

http://www.learnalberta.ca/content/mejhm/index.html ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/video_interactives/integers/integersSmall.html

Link to "Orbit Integers" 

http://www.arcademics.com/games/orbit-integers/orbit-integers.html

Link to Video Games in the Classroom Building Skills in Literacy and Numeracy:

http://www.edugains.ca/newsite/literacy/resource_by_topic.html

Week #4 Reflection

Reflection:

This week we had the opportunity to explore fractions and the difficulty to comprehend  different concepts from both a student and educator position. Fractions present numbers in a new and peculiar way, a form which many individuals may not be familiar or comfortable with. In addition, students are expected to add, subtract, multiply and divide these “odd” numbers together to create a “new” fraction, which I am sure you can imagine how complex and confusing it may be for a new or learner. Even as a future educator, I continue to be uneasy and often perplexed when looking at different fraction equations. This week, we divulged into the issue of nervousness felt by both teachers and students. We also discussed the importance of having both the confidence in ourselves to lead a lesson, while acknowledging that, just like our students, we will make mistakes. To succeed and grow in math we must accept that we are not perfect and realize that it is through our mistakes that we foster our growth as an educator. This lesson has been the most informative and relateable so far, as I feel that encouraging and accepting our mistakes was once something frowned up and condemned. This token of knowledge will become useful in my educational activities studies, as it reminds me that I am not a robot, and if I do make a mistake it will not be the end of the world.

Similar to many mathematical concepts, fractions can be taught in a multitude of different ways. As discussed in my previous blog entries, educators must be willing to expand their horizons when instructing a lesson. This idea is relevant when dealing with fractions as they can such a confusing concept for many students. When we help our students explore their own understanding, we assist them in fostering their intellectual expansion. Another valuable lesson enhanced this week was the importance of including a multitude of manipulators for students. Manipulators allow individuals to visualize and physically work out an equation which they may find to be problematic. An example is shown by the fraction tile sheet (Figure 1) which demonstrates how smaller divisions of a number make up a whole and illustrates which fractions are greater/less than others. For example, when adding together two dissimilar fractions 1/4 + 1/2 one student may find it easier to find a common denominator, and then add together the numerators:

1/4 + 1/2 *4 is the common denominator so you multiple 1/2 by two to get 2/4 so the equation becomes 1/4 + 2/4 which produces 3/4. Some students may be unable to understand this concept and instead use a fraction tile sheet, or a fraction pie sheet (Figure 2) to visually see how the equation works. To conclude, an educator must not limit their student’s exploration of knowledge but instead encourage their exploration of different methods and techniques.

Fractions are concepts which we cannot live without as they are something we encounter on a regular basis therefore, we must continually strengthen and expand our knowledge. A valuable resource I came across can be accessed through the link provided below. The website found in the link below provides a variety of definitions for different equations. It also provides simple and more complicated activities for both beginner and advanced learners. As well, if users make a mistake the website provides an explanation and advice on how to correct it. 

Figure 1                              Figure 2

 

www.rainbowresource.com                            www. learnfractions.wordpress.com/

See link below:

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/fractions/

Week #3 Reflection

Reflection

I found this week’s class and readings to be extremely informative as it spoke about the importance of developing a diversity of thinking for both the educator and students. Through the years there appears to be a flawed conception in that individuals have been reared to believe that there is only one way to come up with a solution when dealing with mathematics. Instead of prompting individual thought and growth students are instructed to follow a specific method to find a solution so that there is a universal answer. This undoubtedly proves to be problematic because what happens to those students who come up with a different way to solve a problem? Are they punished and their voices ignored? This weeks readings focused on the idea of remodeling the "traditional" mathematics classroom by incorporating new ideas and devices available. As well the readings suggests that as an educator we must continually work on expanding our own knowledge because the more we better ourselves the more we have to offer our students. 

This lesson proves to be a resourceful piece for a multitude of educators instructing within the elementary, high school and university/ college curriculum as all students have the right to freedom of thought. Educators cannot expect that their students will all think and respond to a problem in a similar manner therefore individuals must be willing to provide a multitude of possibilities to come up with a solution. Speaking from my own personal experience I know that at times I did not understand how a certain product was produced and came up with my own way to solve the problem. I remember that this was not encouraged which caused me great anxiety as I believed that even though my answer was correct I was doing something unwarranted by my educator. My experience has taught me that it is unfair to punish a child for not thinking like others they are not robots and cannot be programmed to perform in a particular manner. Instead educators should work to foster their ideas and encourage them to continue expand their knowledge and way of thinking. These reliable resources act as an eye opener for those within the teaching sphere. They demonstrate and concentrate on the ongoing problem which continues to be suppressed and what their role as an educator is. It is fascinating to hear the voices and opinions of other professionals as it provides a multitude of solutions to solve the problem. 

The key goal for this week was to speak about the importance of making sure that ALL children, no matter race, gender, age or ability are given the opportunity to understand math. As an educator it is our responsibility to ensure that when students grow nervous we take the time to nurture their needs so that their mindsets can change. When we choose to ignore their issues we are not giving them the support they so rightfully deserve. The readings also reminded educators that it is important to put ourselves in the shoes of our students, to understand and be courteous to the fears and uneasiness they may be feeling. 

As a future mathematics educator I have come to the understanding the significance of developing our patience; not becoming upset or angry when a student is unable to understand what we are teaching to them, as well the importance of encouraging individual thought. When we allow students to come up with their own solutions we are fostering their development as an individual. Although yes it is important that we guide them when they need assistance we cannot tell them exactly what we want, or how to do something as it takes away from their ability to become an independent thinker. This week also touched on the idea of allowing students to work to create their own solutions; to give them a question and tell them to come up with their own answer free from our assistance. We cannot expect individuals to learn if we are constantly spoon feeding them, they have to be willing to take the chance to make mistakes and learn from them. I have definitely been able to make a connection between the readings and my own understanding of what an educator should be like.

https://www.pinterest.com/sunfloursk/math-posters-and-quotes/

Week #2 Reflection

Reflection: 

Mathematics is a subject which continues to undergo heavy criticism and disapproval from a wide audience ranging in race, gender and age.The belief that math is a subject enjoyed by few and hated by many has been ingrained into the minds of individuals and has created the idea that it is a concept which “comes easy” or “naturally” for those lucky few. This negative connotation has left many individuals, like myself, to grow anxious and nervous when having to deal with math and instead of trying to improve their knowledge they choose to ignore it all together. Unfortunately I myself have always had a negative opinion in regards to mathematics as I have never enjoyed learning about it due to my own personal struggle with comprehending different concepts. 

Through my years as a student I have realized that in order to succeed an individual must be dedicate to continually update and improve their skills, be flexible to learn new concepts and be open to share their findings and beliefs with others. Students need to demolish their fear around math and realize that everyone can succeed, that there is hope for those who struggle or need extra help. An individual is their own greatest enemy, if they continually convince themselves that they cannot do something they are inevitably setting them self up for failure. As well teachers must be willing to provide the necessary means of support for their students and continually update their own skills. Teachers act as the most influential figure in a student’s academic year and in order to ensure their success they must be willing to accommodate their teaching strategies and provide necessary guidance for all. When an individual cannot grasp a concept, instead of growing angry or nervous it is a teacher’s responsibility to change what they are doing to satisfy their personal needs. As well, teachers must make math not only understandable but fun for students. From both personal and observational experiences I have learned that there is not one concrete way a student learns. This means that educators must be willing to create a variety of teaching strategies and techniques to fulfill all individual needs. This is what I will strive to do as a J/I mathematics teacher, I will make sure that I offer my students a variety of ways to come up with a solution as well provide a variety of ways to teach them. I took math up to grade 12 so feel that I have a sufficient amount of information however do realize I need to refresh myself on both the simple and complex concepts. 

Report 

The areas of mathematics curriculum that will become my focus in my learning over the next few weeks will be how to develop interesting and informative problem solving questions which encompass a specific unit or concept that students will understand and enjoy. I feel that in order to engage individual interest educators must create a curriculum which satisfies a multitude of audiences. When an individual can relate to what is being taught their level of productivity increases which impacts their ability to succeed. I feel this is often the greatest struggle for instructors as it may be difficult to convey interest in a subject loathed by many. By the end of this course I hope to gain a better understanding of how to make math real so that my students will be encouraged to thrive. 

After completing this weeks readings I realize that as an educator we must be willing to reconstruct the face of math. The article Hollywood’s Math Problem written by Carolyn Y. Johnson acts as an informative piece which emphasizes the idea that math has been given a bad reputation due to the fear and anxiety associated with it. In order to change this mindset educators must be willing to change their ways and accept new ideas and ways of teaching into their classroom. I will definitely remember what Johnson wrote as I feel it to be excellent insight for the expectations of the twenty first century educator. 

https://www.pinterest.com/DDibley/quotes-for-math/

http://www.boston.com/news/science/blogs/science-in-mind/2013/01/30/hollywood-math-problem/QpeSkpnIRPrVyIlJbohBOI/blog.html

Introduction

Hello! Allow me to introduce myself, my name is Kristina Galluzzo. I have recently graduated from York University this past June where I obtained a Bachelor of Arts in English and Humanities. I am currently attending teachers college at Brock University for the junior/intermediate program.

Throughout my elementary and high school years I have never been a fan of math due to my inability to completely understand certain units. I am definitely both nervous and excited to be apart of this mathematics course as I would love to not only learn how to instruct students in a fun, supportive matter but be able to strengthen my own knowledge and understanding. As an inspiring educator I realize the negative images and ideas associated with mathematics and I will work my hardest to try and change these negative perceptions.