Post #1

Welcome to my blog! My name is Bridget and I am a first year teacher and recent graduate of Fordham University, where I earned a bachelor's degree in pure mathematics. I am currently enrolled in Fordham's Graduate School of Education, where I am working on a Master of Science in Teaching in adolescent math education (grades 7-12). I teach Pre-Calculus and Algebra I at Cristo Rey New York High School in East Harlem.

Today I'm going to be talking about my goal of working on the NYSED standard AI-F.BF.1a: Determine a function from context. My goal on working on this standard is two-fold: (1) I want to remind myself of the process of determining functions from context so that I can anticipate what my students may struggle with and (2) I want to become more comfortable with resources that cause students to engage in a productive struggle with the material. Thus far in my teaching career, I have found myself falling into a pattern of giving my students direct instruction and then practice problems solely based on the modelling that I do, rather than encouraging them and challenging them to explore topics and processes.

Last week, my department participated in two days of professional development with the Silicon Valley Math Initiative. Their mission statement is:

The Silicon Valley Mathematics Initiative (SVMI) is a comprehensive effort to improve mathematics instruction and student learning. The Initiative is based on high performance expectations, ongoing professional development, examining student work, and improved math instruction. The Initiative includes a formative and summative performance assessment system, pedagogical content coaching, and leadership training and networks.

The "high performance expectations" piece of their mission statement is important to me because I want to expect high-level work from each one of my students, no matter what their ability level is. Upon reflection, I don't think I've fully found what that looks like in my classroom yet. So, I thought exploring some of SVMI's materials may help. 

I worked through a task that is meant for Algebra I students when they learn about exponential functions. Students are given two tables of values: one represents a linear function and one represents an exponential function. Here is my work:

Aspects of the problem set that came easily to me:

• I could see almost immediately that the flowering ivy growth was a linear function and that the evergreen ivy growth was an exponential function. 
• I anticipate that students will be able to identify the linear function easily.
• I anticipate that students may struggle to put into words why evergreen ivy is exponential. At first, I knew it was exponential by elimination because I knew the flowering ivy was linear. I had to reflect on what it means to be an exponential function and put it in my own words.
• I could easily write a function for the flowering ivy's growth in y = mx + b form. Then, I could easily plug in 3 for x and get the value at 3 weeks. 
• I anticipate that students will also be able to come up with the linear function easily, just from the table. 
• Graphing both functions from the tables.
• I anticipate that students will also find this easy. Students may not draw a curved line through the evergreen ivy points if they do not remember what graphs of exponential functions generally look like.
• Deciding which vine the friend should choose
• At first I put the linear function because I did not realize that it was looking for 8 ft, not 8 inches. I anticipate students making the same mistake. But, once I realized that, I knew it should be the exponential function, even though I hadn't come up with the equation yet.

Aspects that caused a Productive Struggle for me:

• Determining the function for the evergreen ivy growth
• When we had to estimate the height at 3 weeks, I skipped ahead and graphed the function. Then, I came up with ~7 inches. Later, once I came up with the function, I plugged in 3 and got the exact value.
• As you can see from my scratch work, I engaged in a lot of trial and error with trying to come up with the function. Eventually, I realized that the values were a geometric series with a common ratio of 1.5. Then, I had to google the formula for geometric series. After I plugged my numbers into that, I came up with the function.

How my students will need to be prepared before this task:

• They will need to have seen an exponential function before in order to articulate what it means to grow exponentially and graph it.
• They will need to have seen geometric series before and be able to recognize it.
• They will need to be familiar with properties of logarithms, since I used them for question 5.

I found this task helpful because I put myself in the shoes of my students. If I use this, my next task will be to consider my own process and anticipations and find a way to introduce this task and my expectations to my students in a way that will make them feel empowered to engage in the struggle and persevere.

Reflection:

While this task was not of my own creation, it helped me to meet my goal of expanding my comfort zone of teaching and by encouraging my students to engage in high level exploration. Tasks like this will help me maintain high level expectations and require critical thinking in my classroom. 

Upon reflection, even though this task is meant for Algebra I students, I am considering giving this to my Pre-Calculus to remind them of exponential functions. Since Pre-Calculus is heavily focused on interpreting functions, I think that this would be a great re-introduction to determining functions from graphs. I would need to introduce this with an expectation of perseverance from each student. I might even give this packet as an exercise that they work on for the first 10 minutes of class for a couple of days in a row. That way, if they get frustrated, they can put a pin in it and come back to the problem set with fresh eyes the next day.

I think that other teachers should engage in the same struggle that we expect our students to have. Not only does it better prepare teachers to lead this problem set, but it also increases empathy. We will better understand how are students are learning and how they approach the task.