Math Magic

Sometimes when students are presented with problems and solutions in math, they are unable to describe what is happening and mark it up to “magic.” Almost anyone you ask can tell you what the Pythagorean Theorem is, but not everyone can describe why it works. All they know is that it is a magical formula that you use in math that gives you the right answer. Teachers need to make sure that when they are teaching, students understand why the things they are doing work.

The idea of math being magical typically stems from students being told to memorize formulas without understanding how to derive them. We are doing the students a disservice by having them memorize because they lose out on an opportunity to critically think. If students get in the pattern of believing that math is magic, they give up when they come across something they don’t understand because they can’t remember the magical formula they thought they had memorized. Another danger is that if the students do not understand why something works, they may apply it in incorrect ways. We need to teach students to think critically and one of the ways to do this is by showing them how to derive these formulas, so they are not stuck if their memory fails them and so they can properly apply the formulas.

Technology also plays a key role in making math seem like magic. Increasingly, teachers are having students use applets or other forms of technology to make discoveries. In these technologies, often critical features or steps go missing and students do not come to an understanding on why something works but instead rely on the magic of the applet. While these applets can be beneficial to visualizing the concept, they often need to be supplemented. If an applet or other technology-based tool is lacking, the teacher needs to help the students fill in the blanks. Coming up with extra questions not included or giving an explanation for missing information are a couple ways to supplement these tools. We, as teachers, need to use technology to enhance our lessons instead of having it take over every aspect of learning. Sometimes spoken word is needed to reach true understanding.

Even though math sometimes seems like magic, we need to work to make sure that students are firm in their understanding of the “whys” in mathematics.

Building Student Confidence

In the past few years, I have had my share of aiding students with their math homework. Anywhere from college to elementary, I have observed and compared the tendencies of these students. Overall, the students have no issue remembering what they learned, but, if anything, they lack the confidence in their efforts to finding the solution. They answer each solution with uncertainty, looking for any direction from the instructor.

How can we build confidence in our students? It is one thing to have them find the correct answer, but if they continually need our confirmation to find confidence, are we helping or harming at this point? Henry Ford once said “Whether you think that you can, or that you can’t, you are usually right.” This quote helps underlines the importance of having confidence in your own ability, especially in the case of our students. For the remainder of this post, I will discuss a few of the concepts that I have applied to my teaching methods.
Instead of providing an explanation of how to solve the problem, form questions that allow the student to describe the process, helping them consider the question in their own understanding. Asking questions may seem primitive, but good questions can allow students to comprehend and retain the information.

Good questions can also be based in a student’s understanding. For instance, one of the students I helped enjoyed cooking, yet struggled with fractions in math class. By basing my questions and examples on student interests, they were able to base their reasoning in their own terms.

Depending on the relationship one has with the student, it can be intimidating for the student to express thoughts on the subject. Another contributor is the fear of being wrong. More than not, students will mess up when trying something new. In my own experiences, encouraging students to give explanations, even wrong ones, helped them to approach their goal in learning and gain the confidence needed to perform on their own.

Although I have only worked with students one-on-one, I have still seen them grow in confidence as these concepts were applied. Rather than end with some impeccable conclusion, I will end asking for additional ideas, because I wish to continue learning more about this notion. What are other ways we can aid in building student confidence? How does building an individual’s confidence compare to building a class’s confidence? What possible roadblocks are in the way to achieving this goal?

Gamification in the Classroom

            There are over 155 million Americans playing video games regularly. Chances are many of your students will be among these 155 million. To many parents, video games have a negative connotation that seem to have no value. The truth is that video games, in moderation, have many benefits. The gamers use many facts, tools, and information given to them to move on throughout the game. This makes it no surprise that some games can also be beneficial in your classroom.

            In our technology class, one of our favorite type of game is one that sets the students up against each other. If you have competitive students, as we do in Math 371, these types of games can be very beneficial. They can also be used for short quizzes, or exit tickets. One thing that we must be carful with when playing these is that we do not forget what we want our students to learn. Many of these games can teach the students speed, but is speed always important in math?

            Another type of gamification you can incorporate into your lesson plans are quests. During these, the students are given different questions, tasks, or projects to earn points. These are usually done throughout a semester or a month. They allow the students to work at their own pace but also allow your high-achieving students to work ahead. You can even create a fun tradition if you do it year in and year out.

            You can also use badges to reward your student’s learning. One advantage of this could be that not all badges mean the same for the students. A badge might signify an increase of a student’s grade, or an increased level of mastery. The badges will not only encourage the students in the classroom but will also allow the students to see where they are as far as understanding the content.

            In conclusion the main purpose of gamification in the classroom is to engage your students and create a deeper learning while having fun. Not only does it make it enjoyable for the students, it also makes it more fun to teach the content. I encourage every teacher to find a place in their lesson plans for gamification.

How Twitter Became My PLN

Greetings students of Math 371!

I'm very excited to once again add to this blog.  Dr. Vestal asked me two years ago to post as a guest blogger.  I skimmed through my previous post and am happy that it's still relevant.  The revolution is as strong as ever.

I want to talk briefly about how Twitter has helped me become a better teacher. 

I first joined Twitter back in September of 2011.  It wasn't until the spring of 2014 that I started being active on Twitter and using it professionally.  Over the past four years, my use of Twitter has evolved into what I now consider my Personal Learning Network (PLN).  

I first started following some of the all-stars of mathematics education -- Dan Meyer, Andrew Stadel, and Dr. Vestal to name a few.  Over time, I've followed more and more people who I've either met, read about, or heard of via re-tweets and likes.

Each day, I spend between 5-10 minutes skimming through my Twitter feed, fishing for new ideas and resources.  Tonight's catch was okay, with a couple of potential keepers:

If there is a resource or idea that I like, I will simply send myself a direct message of the tweet.  If it is something really great, I'll implement the resource or idea as possible into my classroom.

Also, I will often times search #MTBoS and #iteachmath to see what I can find.  MTBoS stands for Math-Twitter-Blog-o-Sphere, and it is a collection of math teachers who love to share, collaborate through Twitter, and meet in the summer at Twitter Math Camp (TMC).  I have never been to TMC, but I hope to go someday.  Only about 85 people can attend each year; there is a lottery and waiting list for those who don't get chosen to attend.

In addition to providing ideas and resources, Twitter can also provide answers to questions you might have.  For example, just tonight this gentleman had a question he posed to #MTBoS:

Within four hours, there were more than ten replies and a pedagogical conversation taking place about this particular topic.  These conversations can be extremely beneficial to teachers who are in small districts and have no other math teachers in their building to bounce ideas off of.

Over the past four years, I have borrowed dozens of ideas and resources from people on Twitter.  I'm always looking for ways to improve my teaching and being active on Twitter has helped me grow as a educator.  

If you're not on Twitter, I challenge you to sign up today and begin to grow your own network.  I'd recommend these people as a great place to start:

• Dan Meyer (@ddmeyer)
• Andrew Stadel (@mr_stadel)
• Jon Orr (@MrOrr_geek)
• Fawn Nguyen (@fawnpnguyen)
• Michael Fenton (@mjfenton)
• Kyle Pearce (@MathletePearce)
• I Teach Math (@iteachmathAll)
• Classroom Chef (@classroomchef)
• Open Middle (@openmiddle)
• Mark Kreie ;-)  (@kreiem)

There are many, many more very good people to follow out there.
Best of luck on your journey.  I'll be seeing some of you around my classroom!

Mark Kreie

Brookings High School Math Teacher

mark.kreie@k12.sd.us

https://markkreie.blogspot.com/