Deducing Problems In A Math Congress

By participating in a math congress the student role becomes much more active as students take part in a congress where they can discover how other students solved the same problem and ask questions about understanding the various ways that a student can choose to arrive at a solution. A math congress demonstrates a growth mindset where dedication and hard work are depicted in the student's solutions. Students can greatly benefit from understanding that what they bring to the solution is valued and that the teacher does believe in them. 

One of the most important goals is feedback. Once a student can see and understand a problem then they can go further on their path of solving the problem. Often another student may explain to that student where they went wrong or help them to further understand the problem so it is easier to solve. The most important part about solving problems is taking what you already know and applying that information accordingly. Making connections is a crucial step in problem solving. It is important that as educators we provide students with rich problems to support their learning. 

Different groups of students approach problems in different ways and all of them can come to the same solution. In the case of Joel's Kitten Food Problem, some groups chose to focus on the dollar value or the can value, however way the students decided to approach the problem they are still able to come up with the right solution. 

Math congresses allow students to understand every solution and make connections between them. A math congress is student centered and students are able to find out what information is new to them and why they might be able to use one approach versus another approach at different times depending on the problem at hand. A math congress gives students ownership of their own work. Students work better when they know their work and method is valuable and when they have control or a choice. When students make sense of a problem they can solve it. Math congresses allow students to be valuable members of a group and take responsibility; both characteristics that are valuable to their futures. 

For The Love of Fractions

When teaching students about fractions it is important to not revert back to the old methods that were taught to us in the more traditional approach such as cross-multiplication. Students have no idea why they are cross-multiplying and really do not understand fractions entirely with this approach. Instead it is crucial to provide students with good open math problems involving fractions to deepen their understanding of fractions instead of memorizing formulas. Why not simplify dividing fractions for students and let them divide the tops from the bottoms. That is what makes sense and works better for them. I feel that if a teacher in my past had told me it would be okay to divide fractions this way that I as a student would not have struggled or been as frustrated with fractions as I had been. I feel it is important to keep math simple and let the student understand the big ideas so that they can progress in their learning experience and not feel discouraged.

Parallel tasks in the classroom are essential to promote growth in a student's learning experience. Parallel tasks include more challenging or less challenging tasks where students can choose which one they may want to pursue, and then at the end the whole class can participate in a discussion. It is important to not give students generally more than three choices so they do not spend the majority of the time deciding which question to do but stay on task. Students may have off days where they do not feel as great or confident as other days and may want to pursue a less challenging task or students may want to challenge themselves further by picking a more challenging task that day. Whatever the case may be, the student can always pick a question that they can get started on and discuss with their peers.

There are fail safe strategies for creating open questions for students such as begin with the answer to a question and allow students to work on the problem to arrive at the solution. Another strategy used is asking students for similarities or to leave certain information out of the problem and allow them to fill in the blanks themselves. It is crucial to allow students to be scientists and allow them to to try methods out by trial and error. Students can compare answers to see if they are going in the right direction or what trajectory they should take. Fractions can be applied to other units taught in math and you can teach lessons that tie together themes so that students can make connections between the lessons. You might then hear a student say " Oh yeah, I've seen this before. So ratios and fractions are pretty much the same thing!"

Fractions or Ratios or Proportions? How About All Three

There are so many ways of looking at fractions such as it can be comparing different parts of something or parts of a whole. It's important to understand that ratios and proportions are just the same as fractions. There are various types of fractions such as proper or improper, mixed numbers, as well as unit fractions. The most important thing to remember is that coming up with a good problem means getting students to bring up the important vocabulary surrounding fractions such as numerators, denominators, and what fractions mean to them as students. Math is found in our every day life and more specifically we are surrounded by fractions. Getting students to demonstrate fractions in their own ways using manipulatives of all kinds can provide them with a visual representation. A good problem is one that has a wide base where every student can get started and the problem that was demonstrated did just that. Students were able to pick their favourite fraction and represent it in as many ways possible without any rules or regulations. The only drawback to this problem is that there was no real life context provided that can always be a challenge when introducing strands of math.

I thoroughly enjoyed the segment on teaching through children's literature because it proved how math can be related to other subjects as well as how fun it can be for students. The Hershey's Milk Chocolate Fractions Book provides a fun and engaging way for students to be introduced to important vocabulary with regards to fractions as well as an introduction to the strand. What student wouldn't want to learn math with chocolate? It is crucial that fearless speaking and listening is encouraged in the classroom to maximize student's learning. 

A growth mindset is important with regards to teaching math. Providing students with parallel problems gives students with a broad range of learning styles and student readiness to get started on the questions that they want to. It is important to spark up reflection and discussion regarding the problems. Questioning is one of the hardest parts about being a teacher and its important not to give out hints to the student who is asking for help but rather asking questions about connections they have made or getting them to communicate about what they have done so far and what further steps to take.

The Big Ideas from Dr. Small book is a great teacher resource to use. The book looks at the big ideas for every topic taught in school. So often, the specifics of a topic such as math are taught and students tend not to understand the big concepts. The key is to get students to understand the big ideas or larger concepts and have a deep understanding about what they are doing in math and why they are doing it that way rather than just memorizing formulas and applying them without any further reflection.