Editor's note: Those who have followed my math rants know that I am critical of the disconnected math skills taught in schools that take the subject out of context. I also am not a fan of the drill and kill math games like Mangahigh that are more interesting than math worksheets, but pay little attention to the real-world relevance of why these skills are necessary. In this post Brian Marks gets to the heart of the math problem by sharing a resource that puts real-world relevance at it's core.
I can still remember my own math classes as a kid. I remember working out of a text book, listening to my teacher as she taught us three example problems so that we could do problems 1 – 43 (odds only) for homework. Of course problems 1- 43 were all the same problem, they just had different numbers or letters in them. At the time I thought they were just letters, but now I know they were variables. Maybe at the time I knew they were variables, but did I know what a variable was?
Let’s fast forward to the present. What has changed? Often math classes still look the same as they did decades ago. Students enter the room and check their homework, which is followed by direct instruction on some math skill that is meaningless to most of them. Students get to practice a few problems in class and look forward to more homework full of practice problems and maybe some contrived word problems. The only thing different today might be the availability and variety of math resources on the Internet. Students might be using text books less and worksheets more. The Internet is full of websites that provide teachers with skill worksheets that focus on algorithm practice, which means tediously doing the same procedure over and over again. There are even some popular websites that help kids learn the steps to successfully work through an algorithm. On some websites if you get ten of these problems correct in a row you get to move on to a new skill. What is concerning is that many of the math resources on the web are simply making it easier for teachers to teach skill procedures and for students to memorize procedures. We have yet to see sweeping changes in math education in terms of: student learning to conceptual development of math concepts, student discourse, critical thinking, number sense reasoning and a purposeful use of technology, all of which can help prepare students for the challenges of the real world.
How can we help math students to see that math is not a collection of isolated skills and procedures? How can we help them to be better communicators, critical thinkers and problem solvers? How can we engage them in mathematics and help them to see that math is an important tool that can be used to solve real life problems? One online math resource,Yummymath.com, has made it its mission to answer these questions. The website creates and shares authentic math activities that focus on problem solving, critical thinking, intuitive reasoning, student discourse and thinking about math in context. The creators of Yummymath write authentic math activities on sports, entertainment, world news, science, business and much, much more. The site helps teacher and students break away from traditional math classroom routines and helps students see relevance in mathematics and better prepare students for the real world.
Here’s how Yummymath does this and shifts the focus away from skills, procedures and direct instruction.
1. Yummymath activities are written on a real life event, happening or situation that should be a familiar context to kids. Instead of telling students how to solve problems, Yummymath allows students to investigate questions related to a particular real world context and then problem solve and explore concepts within that context. This is the perfect solution for students who often ask the common math question: “When am I ever going to use this?”
2. Yummymath makes use of open questioning techniques. Instead of asking students to simply solve a proportion or find a slope or calculate a mean, open questions allow student to reason, question and think deeply about a math concept. For example, students could be given a mean and then asked to create several different data sets that would have that given mean. Or students could be given the dimensions of an HD television screen and then be asked to give other dimensions of HD and non HD television screens. Open questioning forces students to do more than perform a procedure. This strategy makes students think deeply about a concept. You can learn more about open questioning from the book: More Good Questions, by Marian Small and Amy Lin.
3. Yummymath focuses on concepts, not skills. Procedural fluency is important, but we already get plenty of that in text books and from online resources. A recent Yummymath activity on NFL franchise values provided the actual value of every NFL team in the league. The data was given in several bar graphs, one for each division. Students were asked to look at each division’s bar graph and consider how each bar would look if each team in a particular division had the same value. Students were then asked to redraw each division bar graph, so that each team had the same value. Students could have either transferred value around in the graph, “borrowing” from one team and giving to another or they might have added the values of each team and then divided by the number of teams. The activity asks kids to reflect on their process and helps students to visualize and better understand the concept of “mean.” Yummymath activities focus on conceptual understanding of math concepts. Just as the NCTM and CCSS recommend, Yummymath believes that students should have some understanding of the math that they are doing. Students should have time to explore concepts before memorizing the related algorithms or procedures. This can result in students being able to better judge the reasonableness of an answer when it comes from a procedure. It can also help students to rely less on procedures and more on a deep understanding of the concepts.
4. Yummymath activities immerse students in real life problem solving. Students use actual data or facts to solve problems and make decisions, a process and skill that will serve students well as they enter the real world. Activities such as “The Light Bulbs are Almost Burnt Out” and “Diapers” ask students to use math as a tool to make smart consumer decisions. Many Yummymath tasks ask students to enter into problems with no clear entry point. Students have to grapple with how to make sense of the problem and how to proceed in solving it. The problem is not clearly defined and it is not simply the same problem that the teacher told the class how to solve in the day’s lesson. This is the same process that we go through in our normal lives. When we encounter problems outside of school, we do not have a teacher training us on how to solve the particular problem. We must make sense of the problem and persevere in solving it. “If we want students to develop the capacity to think, reason, and problem solve then we need to start with a high-level, cognitively complex task.” (Stein & Lane, 1996) This type of math problem is called “Doing Math” and it is considered the most cognitively demanding type of math task. Implementing Standards-Based Mathematics Instruction (Stein, Smith, Henningsen, & Silver, 2000).
5. Yummymath tasks are written in a way that will provoke different levels and types of student thinking. For example, in the “Harry Potter Movie Franchise” activity, students use real data to determine which Harry Potter movie was the most successful. The problem is open-ended and allows for students to solve the problem with various levels of sophistication. Activities are set up in a way that promotes student discourse. Students will naturally have different ways of approaching an authentic problem such as this. When it comes time for students to share their mathematical ideas, they will have the opportunity to critique the reasoning of others and articulate their own reasoning. This is one of the eight Standards for Mathematical Practice mentioned in the new Common Core State Standards. Furthermore, these types of activities allow students to enter into two types of classroom discourse as described by Robin Alexander in his research. One type of discourse is discussion, which he defines as “the exchange of ideas with a view to sharing information or solving problems” and the second type of discourse is dialogue, which he defines as “achieving common understanding through structured, cumulative questioning and discussion which guide and prompt, reduce choices, minimize risk and error, and expedite ‘handover’ of concepts and principles” (Research by Robin Alexander, UK, in 2008).
6. Without question students need the opportunity to use technology as a tool in the problem solving process. Several Yummymath activities are built around real life data and encourage the use of graphing calculators or similar programs. Students use this technology in activities like “Monopoly” and “Super Bowl Commercial Costs” to better understand patterns and to make future predictions. Other activities naturally lend themselves to using suggested Internet applications or Microsoft Excel.
Check out this video overview of YummyMath.
If you are looking for a math resource that breaks away from the norm of the traditional classroom resource, one that focuses on authentic math and problem solving, then check out Yummymath.com. Yummymath will help teachers make mathematics relevant and engaging to students. It will also help your students become better prepared to problem solve and communicate and collaborate with others in the real world. Yummymath activities are written to reflect the CCSS and NCTM content and process standards. If you are looking to help your students or child see relevance in mathematics or want to give them an authentic math learning opportunity, use a Yummymath activity with your child, student or class. Check out www.yummymath.com.
Brian Marks is an instructional math coach in Newton, Massachusetts. He collaborates with and provides professional development for teachers. Recently he has done a good deal of work with the Common Core State Standards around both the content standards and the standards of mathematical practice for his school district. He enjoys creating timely and relevant math investigations for his students, his school district, and teachers that believe that math happens daily. He hopes these contributions will help bring current events and increased student motivation to your classrooms.