#meaningfulmath

Miller’s Meaningful Math

Say What? Math Edition

I have done a lot of thinking about an app that is both educational and useful.  I wanted the app to help students in a real and concrete way.  One of the areas I try to gradually help students with is mathematical language and literacy.  I encourage them to speak and use mathematical language with accuracy.  For example, when presenting a group project on limits of rational functions, I have found that students often use the words “top” and “bottom” as opposed to “numerator” and “denominator”.  I do not mark off their grades provided they (as a group) can come up with the mathematically accepted terminology which they inevitably do.  

The “Say What? Math Edition” app would be a tool for all levels of math students to practice and improve their math language skills.  My app will provide the user with an image of a mathematical construct such as a geometric figure, equation, graph, inequality, etc.  The user will then need to put into words what the construct portrays.  The app will then interpret the words exactly as they are said and create a new image.  The app will then let the user know if the two images match or not and depending on the settings, give the user a chance to adjust or correct as needed.  It could also include different modes such as fill in the blank and multiple choice.  I would also like the app to give users the option to share a “brag badge” on social media or via email.  This will allow for students to connect with one another.  This app has the potential to be utilized in many different ways.  

This app provides an opportunity for equity in that users are working to level the playing field regarding the use of mathematical terminology.  It is also equitable in that there are settings to allow for a different number of attempts for the user.  Perhaps a teacher or parent can set the number of tries based on the users ability.  The app should also provide information (written and/or video) regarding missed questions so the user can learn and then correct any errors on subsequent trials.  

There is great importance in speaking with mathematical accuracy.  I interviewed several people regarding this app idea and most said that it is important in some contexts, however in the opinion of some students, it is not as relevant in others.  For example, in places of business it is important to speak with mathematical accuracy.  Students cited examples of errors such as buildings and bridges collapsing and the consequences of injury to people as well as the expense of such tragedies to people in addition to the cost to rebuild.  One student also commented that errors in mathematical language could cause confusion which could prevent someone else from completing a task.  

Another important point was raised by an adult I interviewed regarding voice recognition.  There are many voice recognition tools available for modern convenience and as we look to the future, it is quite possible that voice recognition will become a more integrated part of everyday living.  As such, students should grow in their understanding and practice with speaking to a computer in a mutually understood language.  

According to the students I interviewed, the primary use of their phones is to connect with others.  As such, I wanted the app to match this student interest and provide students with a means to connect to others.  Allowing students the opportunity to share the “brag badge” not only allows them showcase their skills, but notifies students that someone else is able to help them.  If a student has posted their brag badge, they are letting others know that they understand the selected topic and are able to help.  The app can suggest potential helpers to a student in need of additional help.  The brag badge should have a setting that also indicates that the student is interested in helping their classmates, or perhaps the teacher can set that expectation for the class.  

Desmos

Desmos is a wonderful tool for mathematics education.  While I have been using desmos for several years, I have not explored the premade resources.  Through the blog of Dan Meyer (dy/dan) I came across the following resource on the Intermediate Value Theorem.  I introduce this theorem in PreCalculus and like many theorems, it may seem obvious (it does to me).  This interactive exploration leads students to the (arguably) critical component of the IVT which is that the function must be continuous! I have studied and taught this topic multiple times in multiple courses (precalculus/calculus), but the way this activity navigates through the possibilities is beyond anything I have experienced with this topic.  I can’t wait to have my Calculus and PreCalculus students explore this topic!

Interactive Geometry - Here are two geometry tools that students can use to interact with geometric shapes and figures.

Geogabra

Geometer’s sketchpad

These two resources give students the opportunity to manipulate geometric constructs in order to better understand theorems, algorithms, and properties in geometry.

Poll Everywhere

This free tool is a great way to get student responses in real time.  I recently set up a multiple choice poll.  They also offer free response, clickable images, ranking, and word clouds.  The paid version includes reporting features as well as reporting and grading features. There are many ways to leverage this interactive tool in ANY classroom and beyond!

TI Nspire

One of my go to mathematical resources is Mr. Tarrou.  On his website Tarrou’s Chalk Talk, there is a section for TI-Nspire tutorials. Students (and teachers) can use these videos to learn how to effectively utilize this dynamic calculator to help visualize the functions, geometric figures, statistical analysis and more!

Texas Instruments also offers tutorials and other resources.

Extra Practice with IXL

IXL is a good tool for students to practice skills.  Students work toward mastering a skill by solving problems of increasing difficulty as they get problems correct.  Incorrect responses offer students an explanation so that they can improve and hopefully solve correctly on the next attempt. Teachers have access to a dashboard showing how many and which students are currently practicing.  The dashboard also suggests students that may need help.  I have utilized this feature to assist students while circulating the room during in class practice.  This site does require a membership

The above resources all help students become college, career and community readied.  By giving students the tools to visualize and practice their mathematical skills on both an individual and group level, their understanding is enhanced and increased.  Poll Everywhere in particular is a resource that can be utilized in presentations in college as well is into the workforce and even beyond into the community to gather information that can be used to help others.  IXL may be the one example that presents an issue in regards to equity as it does require payment to fully utilize this resource. I recognize that I am fortunate my school has a subscription, but if I did not have this resource available, I would consider trying to obtain the funds as this site is useful for practice and skill mastery.