Video 1: Operations with Fractions

The teacher in this video used a variety of instructional shifts, formative assessment, facilitating discussion, and most importantly focused on understanding the answer instead of simply getting a solution.  He also used a variety of Standards of Math Practices in his lesson.  At the start of the lesson, he used Practice 1, making sense of the problem by showing students two 5 lb. chocolate bars and then he asked if any of them have ever been in a situation where they need to divide up a number of pizzas among a certain amount of friends.  Most of the students were able to relate, and even if they couldn't, they could envision having to split it up.  Right after, the students were given word problems.  Students took different approaches to solving the problem.  Some students drew a model first; others did the multiplication/ division first.  Then, they used Practice 5 which is understanding the solution process rather than on getting an answer.  I liked how the teacher focused the students' attention on ways students used to get the answer and acknowledged different approaches.  He was more concerned as to whether or not the students could explain their thinking than if they understood the way fractions worked.  The final two practices they used were 3 and 4.  They used modeling when they showed their computation of the problems on their white board and on the Smart Board in front of the class.  The teacher also guided their modeling through facilitating productive conversation among the students.  He did not give them answers; rather he asked questions that would spark thoughts that would lead students to deeper thinking about the problem.  He used Practice 3 when he allowed students to construct arguments and critique the reasoning of others.  They were able to ask one another questions about the process they used and explain their thinking using the third practice.

While students were working on the problems, the teacher was walking around asking them questions about why they took a certain step or why they solved the problem the way they did.  This was formative assessment.  At the same time he was doing a formative assessment, he was again facilitating discussion among the students whether it was rhetorical questions he wanted them to think about or questions students could answer among one another.  Instead of giving them answers, he asked questions to get them thinking about the problem.  His shifts were also smooth and he went from one Math Practice to another.  For example, after he gave the real life example of having to split up pizza, he got students' opinions on how they would split up the pizza (using MP1).  Then, he allowed the students to show modeling and then asked the students if they had any challenges to give the student presenting, and the presenter was able to explain their thought process.  This allowed for Practice 3 to take place because they were critiquing the arguments others had.

His main goal was for students to be able to justify how they got their answer.  He wants them to understand the concept rather than solely the algorithm.  He modeled for his students very well and showed his thinking process aloud so the students could learn how to think through the problems.  It is crucial that teachers model how to solve problems, compare the problems to a real world situation, and allow time for students to argue their point of view on a problem and critique their classmates' reasoning.  If they are able to do what was just mentioned, they will show a deep understanding of the concepts and processes they are working on.  Students should be able to collaborate and agree on some aspects of a problem, but also state their opinion if they have different knowledge to share.  He expects his students to know when to voice their opinion but also when to listen, which is also important to keep in mind as a future teacher.  It is not fair to other students in a group if you constantly have one student dominating the conversation and not allowing others to say their opinion.  The construction of this lesson included a lot of aspects of the Math Practices, and it is important to remember to include them so students develop a deeper understanding of math.