## ImagineIT: Phase 3

## Big Idea

The key idea I want to focus on is the big picture of mathematics through student understandings and misconceptions. To develop real understanding of mathematics, I researched the Standards for Mathematical Practice from the Common Core State Standards. There are eight standards but I will only focus on the following three:

Mathematical Practice 1: Make sense of problems and persevere in solving them.

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

Mathematical Practice 4: Model with mathematics.

I choose these three after thoroughly looking at all eight. I have seen the Standards for Mathematical Practice before but never fully incorporated them into teaching. These three are at the heart of what I want my students to remember and use later in life. Each of these practices can be used in other disciplines as well.

The Mathematical Practice 1 of making sense and persevering encompasses the growth mindset approach I want my students to have. Too often I have to students who shut down when facing a challenge because they have never practiced the skills needed to cope. Many students assume they are not “smart” if they do not immediately get the right answer. This shows the disservice these students had in previous math courses where it was focused on procedural and short cuts. By being able to persevere, students will continue to grow throughout their lives.

The Mathematical Practice 3 of constructing arguments and critiques others will allow students to demonstrate their understanding through explanation using evidence and through the perspective of seeing how others approach a complex problem. Many students have difficulty explaining their answer. This stems from the fact that many are just repeating a process and do not understand why they did a certain procedure or short cut. By explaining their understanding, it forces students to move away from the procedural and connect to the foundation of mathematics. Looking at others’ understandings, allows students to correct any misconceptions they have, learn from others and realize that there are numerous ways to solve a problem. Many students think they must solve a problem the way their teacher does. Unfortunately, many teachers reinforce this idea through their grading practices. Varying solution paths should be celebrated.

The Mathematical Practice 4 of modeling connects content with the real world. This answers the famous question of why are we doing this. These are problems that cannot be answered by Google or YouTube. The students must use perseverance to demonstrate their understandings. These models show students why math is important.

Mathematical Practice 1: Make sense of problems and persevere in solving them.

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

Mathematical Practice 4: Model with mathematics.

I choose these three after thoroughly looking at all eight. I have seen the Standards for Mathematical Practice before but never fully incorporated them into teaching. These three are at the heart of what I want my students to remember and use later in life. Each of these practices can be used in other disciplines as well.

The Mathematical Practice 1 of making sense and persevering encompasses the growth mindset approach I want my students to have. Too often I have to students who shut down when facing a challenge because they have never practiced the skills needed to cope. Many students assume they are not “smart” if they do not immediately get the right answer. This shows the disservice these students had in previous math courses where it was focused on procedural and short cuts. By being able to persevere, students will continue to grow throughout their lives.

The Mathematical Practice 3 of constructing arguments and critiques others will allow students to demonstrate their understanding through explanation using evidence and through the perspective of seeing how others approach a complex problem. Many students have difficulty explaining their answer. This stems from the fact that many are just repeating a process and do not understand why they did a certain procedure or short cut. By explaining their understanding, it forces students to move away from the procedural and connect to the foundation of mathematics. Looking at others’ understandings, allows students to correct any misconceptions they have, learn from others and realize that there are numerous ways to solve a problem. Many students think they must solve a problem the way their teacher does. Unfortunately, many teachers reinforce this idea through their grading practices. Varying solution paths should be celebrated.

The Mathematical Practice 4 of modeling connects content with the real world. This answers the famous question of why are we doing this. These are problems that cannot be answered by Google or YouTube. The students must use perseverance to demonstrate their understandings. These models show students why math is important.

## Performances of Understanding

Performances of understanding will occur several ways. In the beginning of each unit, students will journal on a Google Doc about their understanding of the unit’s essential questions. Throughout the unit, we will revisit this journal entry and add to their understanding. At the end of the unit, students will reflect on their understanding and growth through a Google Form. The Google Form will contain rubric style questions where students must self-assess. The form will also contain open-ended questions where students explain their self-assessment and reflect on how they can grow further.

Each unit will have a performance task where students will demonstrate their understanding through creating and sharing a solution to a real world problem. The real world problem will force students to persevere and demonstrate that they can apply their understandings to unknown situations. Students will receive feedback on their performance and then can revise and show further growth. The performance task will give students a voice and ties into the foundation of STEM: explore, create and share.

Each semester students will create their own instructional videos. They can choose from any of the topics covered in the semester or related to what we explored. Students will immerse themselves in the topic like Sal Khan does for his videos. When I introduce this performance of understanding, I will play the video of Sal Khan explaining how he creates a video. By creating their own videos, they are sharing their understanding. These videos will be made public for others on the class and school website.

Daily, there is a class discussion about why our objective is important. The main goal is a shift away from safe answers like, “it will be on the ACT or AP exam” and towards real life examples. I want the students to search for the connections and see how math is all around them. Instead of me giving students examples, I will have the students find the examples. This gives them ownership of their understanding. At the end of each class, we will discuss as a class what they learned, why they learned it and how they reached this understanding.

Other performances of understanding will include Think, Pair, Share, Exit Tickets, Math Talks, Padlet and Google Forms. Weekly, students will submit their favorite mistake of the week. They will share what misconception they had and how they persevered through it. As a class, we will celebrate our mistakes by playing part of the chorus from “It’s a mistake” by Men at Work. This approach will help create a safe environment to take risks.

Each unit will have a performance task where students will demonstrate their understanding through creating and sharing a solution to a real world problem. The real world problem will force students to persevere and demonstrate that they can apply their understandings to unknown situations. Students will receive feedback on their performance and then can revise and show further growth. The performance task will give students a voice and ties into the foundation of STEM: explore, create and share.

Each semester students will create their own instructional videos. They can choose from any of the topics covered in the semester or related to what we explored. Students will immerse themselves in the topic like Sal Khan does for his videos. When I introduce this performance of understanding, I will play the video of Sal Khan explaining how he creates a video. By creating their own videos, they are sharing their understanding. These videos will be made public for others on the class and school website.

Daily, there is a class discussion about why our objective is important. The main goal is a shift away from safe answers like, “it will be on the ACT or AP exam” and towards real life examples. I want the students to search for the connections and see how math is all around them. Instead of me giving students examples, I will have the students find the examples. This gives them ownership of their understanding. At the end of each class, we will discuss as a class what they learned, why they learned it and how they reached this understanding.

Other performances of understanding will include Think, Pair, Share, Exit Tickets, Math Talks, Padlet and Google Forms. Weekly, students will submit their favorite mistake of the week. They will share what misconception they had and how they persevered through it. As a class, we will celebrate our mistakes by playing part of the chorus from “It’s a mistake” by Men at Work. This approach will help create a safe environment to take risks.

## Learning Experience

**CONTEXT:**

I teach mathematics at William J. Bogan Computer Technical High School on the southwest side of Chicago in the Ashburn neighborhood. Three years ago, Bogan began the transformation process for underperforming schools. With new administration, Bogan has grown academically and continues to improve. The student population is about half Hispanic and half Black. Low-Income students account for 86% of the student population, students with disabilities are 20% and English Language Learners are 8%. Academically about 14% of students meet or exceed the standards on the Prairie State Achievement Exam with an average ACT score of 15.5.

Bogan High School was the first 1:1 Chromebook high school in CPS. Every student is assigned his or her own Chromebook for the school year. Technical issues arise at times with wireless internet connectivity but overall students are able to be online. Some days students forget their Chromebooks or it is not charged. This is more a classroom management issue where calling home usually corrects the situation. Students also have the option to receive a loaner from the Chromezone. My classroom has a Promethean Board which works most of the time. I usually have to reboot everything daily in order for it to work.

I am the Mathematics Department Chair and a member of the Instructional Leadership Team. For the 2015-2016 school year, I will teach Advanced Algebra, a junior course, and AP Calculus AB, a senior course. I will have three classes of 25-30 students daily for 50 minute periods. Our school year is divided into semesters.

**CONTENT:**

I want my students to become true mathematicians by making sense of problems and persevering through them, constructing viable arguments, critiquing the reasoning of others and modeling with mathematics. By understanding these three big ideas students learn: what is math? why we study it? how can we better understand it? how math connects to our world and our daily lives?

In the past, my students have had difficulty with all three of these big ideas. Most students are accustomed to the typical math classroom that emphasizes procedures and memorization. In today’s technological, knowledge-filled world, we must go beyond tradition and focus on understanding. A student cannot compete with Google for knowledge but he or she can have greater understanding. I want my students to persevere through difficulties, explain their reasoning, understand the arguments of others and see how math connects to the real world. All of these skills will produce a lifelong learner who is able to take on any challenge.

**PEDAGOGY:**

Problem-based learning will work best pedagogically for my content and goals. Through problem-based learning, students will explore, create and share their understandings. Developing an approach like the 3 ACT Math by Dan Meyer will create curiosity in the student. We will start with the “huh?” moment then continue to add on to it until we reach the “wow” or “aha” moment. Students will sit in groups to collaborate on their understandings. This type of learning forces perseverance since the answer is not from memorization of facts. Students have to synthesize their understanding to develop a coherent, arguable solution with supporting evidence.

We will use Think-Pair-Share as we develop new understandings. Independent work will occur when students journal about their understandings and misconceptions. As a class, we will use growth mindset to celebrate mistakes by playing our mistake song. Growth mindset will also be observed when students share their favorite mistake of the week and how they grew from it. Each semester, when students create their instructional videos, collaboration will be key.

**TECHNOLOGY:**

Students will use their Chromebooks to explore, create and share their understandings. The Google Apps for Education will be essential in this process. I will use Google Classroom to disseminate the assignments and Google Sites to share the daily Google Slides, resources and class calendar.

I will use the Promethean Board to project the lesson every day. The lesson will include slides for students to discuss the importance of the objective at the beginning of class and reflect on what they learned at the end of class. Students will also use the Promethean Board to demonstrate their understandings to the class. Google Docs will be used for the student journals and the Favorite Mistake activity. Google Forms will be used for end of unit reflections and other formative and summative assessments like exit tickets. We will use Padlet for Think-Pair-Share and classroom discussions.

For students to create their own instructional videos, I am still figuring this one out. We could use SnagIt from TechSmith to screencast on the Chromebook but I need to play around with it more and see if there are any better options. I also want to give my students freedom to create the videos they want. SnagIt would not allow for students to annotate over the screen. Another option is to use an iPad cart and use Educreations for annotating.

By using Google Apps for Education, students will create a portfolio of their understandings and creations on Google Drive. This can easily be shared publicly by creating a Google Site. I want my students to be able to “take” the portfolio with them. I need to find out if you connect a separate Gmail account to the Google Site will it save the work when the CPS email account is erased after high school graduation. By sharing their work, students are making their understandings public.

Through the content, pedagogy and technology, students will be able to become real mathematicians who explore, create and share their understandings.