Video Blog Three

This set of videos main focus was on solving and understanding algebra and understanding the formulas and the reason why the formulas work. The videos gave three examples of lessons used to teach algebra. All the lessons used manipulatives to help students understand the concept of algebra. Also, the lessons given could have be adapted to any age/grade/ability level, which was great. The first lesson was having students look at the V-pattern of how geese fly and having them come up with a way of figuring out how many geese there were besides counting each individual goose. The students were given manipulatives to solve this problem. Students were able to bounce ideas off of each other, so communication was also a big help in solving this problem. The second lesson was having the students view beams used for construction and and figure out the pattern of how each beam was laid and how it differed from level to level of beams. Once again, students used manipulatives to help them solve this problem. Students were given tooth picks to make their own beams and help them discover a formula for this type of problem. This lesson was very authentic and holistic for each student because each student had their very own lesson. The whole class had different formulas. The teacher took advantage of this situation and discussed with the students how even all of these equations look different, some of them are the same. The third and final lesson displayed in the videos was very interesting and had the students keep track of the rate of hair growth. This portion of the videos was interesting because the teacher had the students relate this to real life, but also had them create a formula. Throughout the videos, both NCTM and the CCSSI Standards were practiced.

NCTM Process Standards:

• Communication: Throughout all the videos, communication was heavily displayed. In all three lessons, the students worked in small groups to create a formula to solve the problems. Then the students and teacher would have a whole class discussion, where they students will ask any questions they may have and discuss their findings. Having students work in small groups and then the whole class works on different types of communication.
• Connections: All three lesson plans did an excellent job connecting the math concepts to real life. In the first lesson, students connecting the pattern of how birds fly to mathematical formulas. In the second lesson, the teacher connected formulating formulas to construction beams, and in the third lesson the rate of hair growth was used. The variety of ways mathematics was connected to the real world is beneficial because it will reach out to more students.
• Problem Solving: Problem Solving was displayed in all three of these lesson plans. Students needed to formulate a formula and equation to solve each problem. They were given manipulatives to help solve the problem.
• Reasoning and Proof: Students were working in small groups and explaining the formulas and equations they created. They each needed to give reasons how they came up with their equation. During the whole class discussion, the teacher made sure to ask higher order thinking questions pertaining their equations.
• Representation: Students were given manipulatives to help them solve the problems. Manipulatives brings the problem to live and helps the students really picture the problem. An example includes using toothpicks to represent the number of construction beams and to figure out a pattern of how each beam is laid at each level.

CCSSI Standards:

• Construct Viable Arguments and Critique the Reasoning of Others: Students worked together in a variety of group sizes (partners, small group, and whole class) to decide on one way to form the equation. In order for students to agree on one form of an equation, students needed to justify to their peers their reasons behind their equation.
• Make Sense of Problems and Persevere in Solving Them: Students were able to use manipulatives to help them find the answer and create a formula. Once the students found a way to formulate a formula they were also able to use the manipulatives to solve the formulas. The manipulatives also helped the students communicate and tell their classmates why this formula would work.
• Model with Mathematics: Throughout each lesson, mathematics was displayed. Students used manipulatives to help solve mathematical equations and formulas.

I thought these videos were great, I really enjoyed seeing the students engaged during these lessons. Typically, math is a subject not many students enjoy, but these lessons definitely make math a more enjoyable subject. The class didn't have textbook work and handouts, which is awesome, because that is how I remember most of my math class career. Having such hands-on lessons makes the learning process more authentic, and helps students retain information for longer periods of time. Throughout each lesson, a variety of NCTM Process Standards and CCSSI Standards were displayed which is fantastic, and helps develop multiple strengths not only in mathematics but other subject areas. Using manipulatives also helps students who learn best by visual aids, and students learn best when they can relate something to their outside world, and all these lesson did exactly that.