Weekly Report & Reflection Week #6

Proportions

       This past week my class covered a until lesson on proportions.  I wanted a bit of refresher on the subject so I went to the Math Antics channel on YouTube.  Lately, I've been using Math Antics quite frequently.  It has been a useful instructional tool, helping me to brush up on my mathematical knowledge and skills.  The strength of Math Antics as a learning tool is the way they present each problem.  The math lessons they provide are very clear, slowly delivered, and gradually progress in difficulty.  For example, in the video on proportions above the instructor first provides a reminder of what fractions and ratios are before moving on to define proportions.  His first lesson on proportions explains the technique of cross multiplying to find an unknown value.  This lesson attempts to be as simple as possible, allowing students to gain a basic grasp of how to find unknown values in proportional problems.  Following this, the second lesson is a little more difficult.  Applying proportions in a practical way, the instructor uses the example of a map of Hawaii to show it's proportional relation with the actual island of Hawaii.  This lesson proceeds to explain how to find an unknown value by using division.  Overall, what is presented is a clear and concise lesson on how to understand proportions and how to calculate unknown values in proportional problems.

       Learning proportions is a requirement for grade eight in the The Ontario Curriculum, Grades: 1-8 Mathematics.  A specific requirement of the curriculum states that students should be able to "solve problems involving proportions, using concrete materials, drawings, and variables" (Ontario Curriculum, 112).  In the Math Antics video supplied above the instructor provides a good example of this specific curriculum requirement when he employees the use of a map.  Using the map to calculate proportions is a good practical lesson that can be used with students.  

       For example, a fun exercise might require students to break up in to small groups.  Each group is given a map with a list of cities on it.  Group members are to imagine they are a flight crew travelling to each of these cities listed in the specific order or "flight plan."  Using what they know about proportions each group must calculate the total number of kilometers traveled by their flight crew over the course of their entire journey.  Each group could have different flight plans or even maps of different proportional sizes.  The group that calculates the correct total amount of kilometers they have traveled wins a prize.  If there is time left after this activity student could be asked to estimate how far away they think a particular city is (e.g. how far do you think Hamilton, Ontario is from Vancouver, British Columbia? Etc.).  Students can then measure and use their working knowledge of proportions to find out which estimation is the closest.  First to find the calculation correctly and closest estimation gets a prize.

     In closing, I will add a few final thoughts about Math Antics and it's potential instructional value.  In particular, one possible use for instructional videos like Math Antics is it's potential to be used in the flipped classroom model.  Students can view this video prior to class, devoting more in-class time to questions and, for instance, the flight plan activity example I have provided.  By employing the flipped classroom model and using sources with quality videos like Math Antics, instructors can devote more their time to organizing meaningful activities and helping students that are struggling with comprehension.

Weekly Report & Reflection Week #5

I have decided to dedicate my blog post this week to our mathematics unit on Great Games.  I just finished the requirements for this assignment (posting on three games and commenting on two posts about games), so I thought it would be appropriate to write a few words on what I have taken from this experience.  In general, I found the unit to be quite rewarding.  Its intent is to help incorporate gamification (applying elements of game playing to activities) with educational teaching strategies.  I believe gamification can work as a valuable tool for Twenty-First Century instructors.  In my opinion, its greatest value is to provide students with educational material that is engaging, entertaining, and interactive.  The games that I experienced tended to be free to users and available online.  Some were simple and basic (for example, check out the game Puppy Chase), while others were complex and required a lot of investment (for example, check out the game Prodigy).  Significantly, the games cover a variety of subjects that relate to the specific requirements set out in  The Ontario Curriculum Mathematics Grade 1-8.  That is, there are games available for additional and subtraction, integers, fractions, multiplication, division, and so on.  Furthermore, it is possible to find games with various subject matter and levels of difficulty that would be appropriate for a wide range of age groups.

I think that incorporating gamification with mathematical educational is a wise instructional strategy.  Sadly, students often complain that learning mathematics is boring and disengaging.  However, I believe gamification can help to rectify these often hastily assumed opinions.  Gamification has the ability to get students interested in learning by challenging them in creative ways.  Furthermore, if the games offered to students are good enough it is likely they will invest a lot time in them.  It is often difficult to get students to invest a lot of time in to further developing their understanding of foundational knowledge.  Gamification may be a technique that can help to improve this problem.  Realistically, I do not think gamification is a kind of magic bullet for solving educational instruction, but I do think that when students enjoy what they are learning they desire to learn more. Therefore gamification can act as a great facilitator for increasing student interests while simultaneously improving their basic skills and knowledge.

clipartsheep.com (public domain) 

Weekly Report & Reflection Week #4

This week I have chosen to reflect on my Mathematics Learning Activity Presentation. My presentation was around fifteen minutes and focused on the subject of decimals. This was a novel experience for me.  Previously, I have presented to a class on numerous occasions, but not on the subject of mathematics. Since this was new territory, proper preparation and structured organization was an absolute necessity. To achieve these goals thorough research of the subject matter and careful choice of instructional method were a necessity.  The sources I used for my research were the Ontario Guide to Number Sense and Numeration: Grades 4-6 and Making Math Meaningful to Canadian Students, K-8. Both of these texts were very useful in supplying various formulas and methodologies for explaining how decimal numbers can be added, subtracted, divided, and multiplied. I also discovered a few useful tools in the Ontario Guide.  In particular, the 'hundredths wheel' and 'number grid' located inside it can act as a useful visual aid for students.  While the information and strategies found in both these books were more then sufficient for planning my presentation, I also decided to research about decimals on line so I could find out what is out there and brush up on my knowledge a bit further. In my search I discovered Math Antics on youtube. Math Antics' Fractions and Decimals Lesson was a useful refresher course on the basic decimals operations mentioned above.  Having achieved my research goals, I felt confident enough to begin planning my presentation.

From my personal experience with mathematics, some of the most engaging lessons are collaborative and interactive. However, I currently lack the technological know-how of instructors like Dan Meyer, therefore a simpler approach for my presentation was required. For this reason I decided that my presentation should involve a collaborative group project combined with a lecture. I wanted the group project to have relevance to the actual world, so I thought the typical monetary interactions of a cafe server worked nicely for incorporating the use of decimal numbers. I came up with various problems involving the adding, subtracting, dividing, and multiplying of decimal numbers, or, in this case, money. I also attempted to be careful to present the various problems and solutions in terms of equivalences between decimals, fractions, and percentages. Finally, I incorporate the hundredth wheel into one of the questions for the group assignment.

Overall I found my experience of presenting to be beneficial. It gave me some much needed practice, both in presenting and planning lessons on mathematics. However, there are some areas where I will aim to improve next time. My first area that I have marked for improvement is time management of the presentation itself. I exceeded the time allotted me, which forced me to rush through the end of my lecture. This was due primarily to the time spent on the collaborative group work taking place prior to my review of the solutions. Before my next lesson I will time my presentation beforehand, or perhaps engage the class in a teacher-student interactive model and thereby cover the questions collectively. It was also suggested to me to use the hundredths wheel more inclusively with entire group assignment, rather than just for one particular question.  This is a useful insight as that would have provided further engagement for students as well as to fully diversify the learning model to include visual aids. With all this in mind, I look forward to my next presentation where I can learn from these experiences and apply the knowledge I have gained.