Week #6 Reflection

This week in our mathematics class we furthered our investigation on the topic of ratios, rates and proportions. To begin we were given different questions which we worked on independently and then reconvened as a group to discuss different ideas produced and thoughts generated. This is a great technique for instructing as it gives enough room for both independent work and group discussion. We continued our lesson by looking at the how rational proportions are similar to fractions in that they are used to compare or relate numerical values that are equal to one another. Similar to fractions this unit presents numbers in an unfamiliar for many individuals therefore it is important that educators take the time to provide students with a variety of methods to compute and understand what is being taught. To benefit the greatest amount from a lesson an educator must make a lesson practical and relatable for their students. When a student feels that what they are learning is beneficial towards their everyday life they are more likely to succeed and be inspired to learn.

This idea was demonstrated in our lesson when we were introduced to “Joels Kitten Problem”. This activity required individuals to work together in groups of two to four and come up with our own method to solve the problem. As a group we were responsible to solve the question and write out our steps with clear details on a piece of chart paper. When this was complete we joined up with a new group were we were responsible to instruct others on what we had done and communicate our way of interpretation and thinking. The benefit of this question was that it was open ended, it allowed for a variety of unique solutions and thinking techniques, as there was not a definite way to produce an answer. This method of teaching was informative as it was fascinating to observe the variety of thinking techniques. For example my group solved the problem through trial and error whereas the group we partnered up used fractions (Figure 1). Although our techniques were completely different, we both came up with the same conclusive answer. I thoroughly enjoyed participating in this exercise as listening, explaining and communicating with fellow peers not only strengthened my knowledge but expanded my overall understanding of the lesson.  As a future educator I anticipate including this technique in my classroom as I feel that students learn best from one another and benefit when they are put in an instructional position.

In my prior blog post I discussed the importance of including interactive, educational games into a lesson in order to satisfy the twenty first century practice of learning.  This week I explored the resources provided by our professor however continued to explore the outlet as I wanted to see what else the website offered for users. One game which I found particularly interesting was “Ratio Blaster” (Figure 2) an interactive game which worked to enhance students understanding of rational equations. Users are given one minute to complete as many equations as possible in order to proceed to the next level.  When a question is answered correctly the ships you are shooting at remain still however answered incorrectly the spaceships move closer to your shooter. The equations were not complex and when answered incorrectly, the correct answer was demonstrated. Unlike the resource “Orbit Integers” I explored last week this game was not a race, which may be beneficial for students who cannot handle a more fast paced game as well when a question was answered incorrectly a new solution was not produced instead the same question was asked which allowed individuals to fix their wrongdoings. As twenty first century educators it is our responsibly to introduce students to the abundant amount of resources available to them. We must take the time to discover different resources as they will have numerous benefits within a classroom.  

Figure 1

A screenshot of my group and a peers group solution to the question presented in class. Both solutions demonstrate a wide range of thinking however the final answers produced are similar.

Figure 2

A screen shot of "Ratio Blasters" users aim to "shoot" the correct answer for the question provided. The space ships lower when a question is answered incorrectly until they reach the users blaster.

Link to "Ratio Blasters"
http://www.mathplayground.com/ASB_RatioBlaster.html

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/