Math's Competitive Side

I have played on many sports teams during my high school years and so I think it is safe to say I thrive on competition. When one thinks of competition the polar opposite thought might be mathematics, well I am here to tell you are WRONG! “Mathies” can get competitive too I have seen it first hand and it is intense. I have experienced a number of student competitions within the field of STEM that students can get excited about and in the same way as a basketball tournament these competitions require practice, hard work, and commitment from the team. The first example is the Jr. Math Challenge presented by the Hamilton-Wentworth Catholic Board. This bi-annual event brings students in grades 4-6 together to learn and compete in all things math. Six students from each school (2 from each grade) are selected to represent their school at this one day tournament. In preparation for the event teacher coaches usually practice all types of math problems with their students. The format of the event is as follows; schools are ranked based on their scores, scores are received from their participation in each of the activity rooms. Some of the rooms the students participate in exercise student mental math, problem solving, critical thinking, and collaboration skills. Students are awarded with prizes and also have the opportunity to listen to inspiring speakers in the field of STEM. A new similar contest has been created for high school students. The Mohawk Math Engineering Challenge is held at Mohawk College and has been created for grade 9 and 10 students to encourage students to continue a path in STEM. In its inaugural year this contest partnered with a number of sponsors to provide amazing tech prizes for the students. Another contest present in many southern Ontario high schools is the Waterloo Math Contest presented by the University of Waterloo a leading university and math and sciences. This contest is simply a test students that can write to extend their math knowledge and their scores get ranked within their school as well as province wide. An example of a large scale competition is any of the Robotic meets. These are the ultimate events that combine a love for STEM and sport. In these competitions high school teams bring their robot, which they designed and built, to a stadium which is transformed into a playing field where their robots are to complete a series of tasks. This is not just a show and tell event where students show off what they have done, they need to show what they can do by pinning their robot against others in the field and usually race to complete the tasks. Students are on their toes at these competitions as they are constantly making adjustments to their robots and their strategy to the games. These competitions truly demonstrate next level intelligence in students and they only get more impressive as you enter regional and global competitions. There are so many opportunities for students in STEM to show her competitive side and why not!

Movie Math

One important aspect of being a math teacher is getting students to recognize the usefulness of mathematics and possibly inspiring students to pursue a career in STEM. One way to achieve this goal is to provide students with positive role models in STEM they can look up to. Being a “mathie” and a movie buff myself, I have seen a number of movies that inspire me as a mathematician and can do the same for students in my classes. Below are some films that I can see showing or referring to my senior classes.         

This first film is not only inspiring to students pursuing STEM but specifically to female students. Hidden Figures is a recent Oscar nominated film celebrating women who have made significant contributions to math and science. The story follows African-American women working at NASA as Mathematicians and a Physicist. These women were integral to the success of sending the first American astronaut, John Glenn, into orbit. Although this movie takes place in the 60’s it demonstrates the gender disparity within the field of STEM. For female students it shows that yes there are opportunities in this field for them and they should be confident in their own intelligence as well as their passion that this career is for them despite being outnumbered by males.   

The Imitation Game depicts the historical events during World War II as British intelligence agency hires mathematicians to break a Nazi code. As much as this is a World War II movie, the focus is on the group of mathematicians that are on the clock to build a machine that will break the code. This movie proves the usefulness of mathematics and may intrigue students to further investigate the world of combinatorics. The movie also provides a strong female lead that uses her intelligence to help solve the code.      

The Man Who Knew Infinity is a movie for true math people. The plot surrounds the life of now famous mathematician Srinivasa Ramanujan, who originally travelled from India to England to work with a professor in the math department. Ramanujan had produced solutions to many unsolvable problems as well as providing proofs for his own theorems. This movie demonstrates the endless possibilities of mathematics. It would be useful to show this movie to your grade 12 students as it explains the importance in proofs and providing information to back up your calculations as this is what they will most likely be exposed to in university.  

Moneyball is a light hearted film which once again demonstrates the daily applications of mathematics. The movie is about the general manager of the Oakland A’s Baseball team that decides to incorporate a statistical approach to recruiting and running his team. This mathematical approach to baseball is now being applied to many of the MLB teams today. For students who love sport and math this movie shows that there are a vast number of job opportunities in mathematics and there are opportunities to work in a job that combines your passion for sport and math.  

Lastly, 21 is one of the classic films combining probability, chance and crime. This fictional movie follows a university student who is recruited by his professor to join an elite “math club”. What this student was not expecting was to find out that the aim of this club is for the students to use their math skills and take them to Las Vegas to win big at the games. For any Data Management course, this movie shows and explains a number of the concepts learned and then expends on them further. 

Money Matters

In this blog I am sending a message to all coders, app and online game creators and website designers. I have been working with some students in locally developed high school math classes and I have found that there is a shortage of good engaging, interactive math games for students working at this level. The focus for locally developed classes aside from preparing them for the grade 11 workplace course is to develop the mathematical skills that can transfer to crucial life skills. The most important of these skills is financial literacy which even the Canadian government has recognized as an important aspect of education we need to be focusing on. I was recently teaching a grade 10 student who wanted to develop her money skills. The first and obvious strategy I would suggest to all teachers is to use a cash register, yes the old fashion ones we played shop with in kindergarten. The best way for students to understand the value of money and spending is to physically practice. During our study sessions, my student and I would work through class homework sheets and solve written financial problems by adding and subtracting values manually and drawing pictures. Then we would re-do the problems but this time completely orally and using the cash registers just like in a store. The first few times there was definitely a disconnect between the idea of written monetary values and having the physical dollar amount in their hands but with practice it was a seamless transition between paper and practice. This is a great way of learning but it cannot be the only way. I found after a while the students were tired of using money the same way for every question. I tried to incorporate some practice using technology but getting to the root of my problem, the online games I found sucked! All the free online games were too simple, they repeated the questions, and they were asking students to perform the same type of transactions. Then I would switch between games to find different problems but most online money games showing students the coins and bills are mostly American. Then looking into apps and computer game, the best ones were super expensive and others were hard to find. I know school boards do have licensing for some excellent games but how does this help the parent at home or in the summer when they want to practice math skills with their child without breaking the bank. Yes if you search there are good worksheets and activities available online to engage students but for those who are more inclined to practice with online games we are still waiting for a great Canadian invention. One final note to add for parents, take your kids to the store with you, not just to pick out what they like and then help you with the grocery bags. Get your children to shop with you, look at flyers, compare prices, write a list go to the store and do the math before you reach the checkout.  

Math Online?

Hello blogosphere! I am back with a few more things to say surrounding all beautiful things math.  My first topic of discussion is e-learning and mathematics. The shift towards blended classrooms, flipped classrooms and online courses are most the most predominant trends in teaching math. With that being said, there still many people including teachers that question the delivery of course content and student success rates from online math courses. As a student I have personally not experienced an online math class however there have been a few variations I have encountered as a university student and as an educator. In university some intro calculus classes for programs other than math and science were offered online. In these courses students were taking online quizzes, listening to online podcast lectures and submitting assignments online. This course was run through the university’s main online portal “Avenue To Learn” however the course was only partially online as there was a traditional in-class portion each week. This format also required students to write all tests, mid-terms and exams in person on campus. This course was clearly more of a blended approach and since the students enrolled in the course most likely did not have a strong math background they found they should still include a traditional in class portion. Looking at the high school level I have experienced multiple fully online courses using the online hub “Desire to Learn”. These courses especially during the summer are always full and the subject areas offered are usually English, History, Geography, and some of the upper year social science courses. I have yet to see a Mathematics course offered online and there are a few reasons I can see why. 

https://qph.ec.quoracdn.net/main-qimg-db1bf4e3b3806096cfe1e2d853a10e3d

First, just like the university students, high school students may require individualized attention and assistance that is best provided in person rather than through a screen. I think in using this portal makes it difficult as a teacher to really get to know your learners and to understand where they are struggling. This places a lot of responsibility on the student to advocate for their learning and make sure they send emails to their teacher and pose questions within class forums. Some arguments have been made from students and teachers that this online forum and others similar are difficult to work with, confusing and overall not very user friendly. I believe this comes down to the effort put in by the instructor. I have seen a history class that was designed in an extremely organized fashion allowing students to follow instructions that were very explicitly written. The site also incorporated links to videos, webpages and other sources used to aid the lesson, all of which were not difficult to locate later on and it did not put the students through a maze to get back to the lesson they were working on. Again, this was a mostly writing based course and the question remains as to whether even the most organized and well planned sites can effectively educate students in a mathematical sense. This brings me to my recent experience with Google Sites and Webinars. I personally believe that in catering to all types of learners an online mathematics course should include both an interactive face to face component as well as individual study. Google Sites and Google classroom are excellent bases for math classrooms. A teacher is able to engage students with visuals, maps videos, provide links to games, blogs, and other helpful or interesting math links. I know you can do most of this on the other portals but having the information on a website you may be more likely to get students to participate in readings and additional learning activities instead of looking for what it due for the week. Using this method I think including webinars can be a solution to connecting to your students and understanding their fears, struggles and goals in the class. For example you can provide the link to webinar session to be hosted once a week and students can join in to ask questions, discuss their learning and possibly working on their problem solving skills together as a group. As new programs continue to be created and curriculum is developed there are endless possibilities for online learning, yes even in math as long as there are dedicated teachers, committed learners and an open mind.   

https://www.engineering.com/Portals/0/BlogFiles/swasserman/bigstock-E-learning-slogan-poster-desig-35724818.jpg

         

Activities for Workplace Math

College math classes will bring you a variety of learners. Among them will be the students who are taking their last math class ever and they really have not patience for math. This brings your challenge as a teacher to keep these students as engaged as possible and provide as much evidence for your students on how learning math will benefit them in the future. The activities presented last class did an excellent job in achieving this. The first activity presented was a finance lesson geared toward the grade 11 MBF 3C class. This activity takes place the day after teaching the class how to calculate interest. In this activity, student groups are provided with the terms and information on different credit cards. The teacher then provides a scenario to the entire class where something is purchased and based on their information each group needs to calculate their interest and the benefits of using this credit card plan. The class then compares the results and discusses their thought on the benefits and disadvantages of credit card plans. Using actual credit card and debit plans is definitely a benefit for students as this develops life skills for everyday budgeting and banking.

The second activity was directed towards grade 12 MAP 4C class, it also developed student knowledge directly applicable to useful life skills. This activity allows students to design a house plan and make decisions based on a budget. The teacher provided a floor plan with dimensions of each room and students could choose from an array of tiles, hardwoods, carpeting, and paint colours to decorate their home. A worksheet is also provided for students to calculate the total cost of each room after they make their decisions. In class we were to choose three rooms and calculate the total cost however it was mentioned that this would make an excellent culminating assignment with a few adjustments. Some of the changes that could be made are 1)have students complete the entire floor plan 2) re-calculate some rooms using different materials and compare prices 3) Have students discuss the accuracy of their estimates i.e. some of the missing variables in the activity such as hidden costs/savings.

 

Math Gamification for Senior Classes

In my last math class, my fellow teacher candidates presented lesson activities that were excellent examples of incorporating gaming aspects into the classroom. In senior classes it can be a challenge to make math fun for students but I can tell you that these two activities had an entire class of adult learners completely excited about playing games.

The first activity presented by my colleague was "Deal or No Deal" for the Data Management course. In this activity student groups will be re-creating the Deal or No Deal game show and like the premise of the show they will calculate their probability of receiving an enticing offer from the banker. There was a lot of prep work done by the teacher. In each group is provided with a bristol board of cases, offer cards and 3 handouts for calculations, reflection questions and to outline the rules. After students chose the specified number of cases they were given an offer from the banker and the they to calculate probabilities of the having a case with a value greater than and less than the offer. Based on these probabilities students would either make a Deal or No Deal.  Overall I thought this was a very fun and useful way of practicing basic probability. For future use I would try to experiment with ways I can transfer some of the game components to an online version. One way I can already see working is playing this as a class and having the case board on one PowerPoint.

The next fun activity was a classic game of "Dominoes" and the activity was geared towards a Grade 12 Advanced Functions class so the faces on the Dominoes were Logarithms. Personally I had never played Dominoes before but it is very easy and for math people very addictive to make a match. This was an excellent way for students to practice their log laws. My colleague explained that in her class she actually used this as a warm up activity after just teaching the log laws but it can also be used later for review. Also, each time they play students can assess how they are progressing in their knowledge of log laws by tracking how much time it takes them to convert the logs to a single value. This activity can be adapted to almost every math course, instead of logs you can have equations in different forms, trig equations and angles, and solving for x.    

Grade 11 Functions

Grade 11 Functions is always a tough course for students whether students go from 10 academic to 11 University or 10 academic to 11 U/C the grade 11 curriculum does have a jump in the learning. Students in grade 11 will learn new/larger concepts and are required to practice through a range of application questions. One of the main new concepts in the grade 11 curriculum is exponential functions. This week one of my colleagues presented an activity to be used as an introductory lesson to exponential functions for a university level class. In this activity there were three stations created where each presented a problem that could be modeled by an exponential growth function. Being an introductory lesson the students are unaware of exponential growth applications or how exponential functions are represented. Thus students use existing mathematical knowledge and strategies to solve for the questions provided at each station. I really enjoyed the specific application questions my colleague had created for the students which were all very engaging and related to the interests of high school students. Examples included zombie apocalypse rate, ice bucket challenge and number of folds on a paper. For the first two stations, in order to solve for the number of people (infected or involed in the challenge) after x many days, there were counting chips provided. This helped the students visualize that there was a growth occurring however it was not linear or quadratic like they had already seen. The other station provided physical sheets of paper  for the students to fold and record the squares created after each fold. Overall this activity was very useful as an introduction as it forced students to not only apply previous knowledge but also use critical thinking to lead them to exponential functions. Although this was created for university level class I see it also being useful in a university/college level class.