## ImagineIT: Phase III

Phase 3: Action Plan for Advanced Algebra 2015 – 2016

1. Identify Desired Results:

From what we studied this summer, I realize I need to shift much more of my teaching to showing the applications of the concepts we are studying, especially with the Advanced Algebra students. Many of the students in Advanced Algebra will have shown signs of struggling in Algebra and/or Geometry. Many of them do not feel math is their best subject or even one they care to study. Since many of their classmates from FR and SO year have chosen to take Honors Advanced Algebra, their feelings are reinforced that they can’t do math. I have taught all levels of courses from Double-Period Algebra 1 to AP Calculus. I enjoy teaching AP Calculus because of the deep level of mathematics. I have always enjoyed mathematics because of its beauty and elegance, the way concepts overlap and fit together. I realize not all of my students share this same love for math and need to focus on the “usefulness” of mathematics, the importance of its application. Really being able to answer “When am I ever going to use this??!!”.

The focus in most Algebra 1 courses is order of operations, operations with signed numbers, simplifying and evaluating expressions, solving linear equations, and usually ending the year with solving quadratic equations. The focus changes slightly from school to school, depending on how much pre-algebra is offered at the lower grades.

In my Advanced Algebra course, I will be beginning the year with a review of linear equations. We will spend time graphing lines, analyzing slope, drawing lines of best fit, and focusing on the applications of linear equations. Most applications involve phone plans, car rentals, prices for parking, and distance/rate problems. Most students are fairly comfortable with these scenarios since there are few parameters in the equations and they can easily relate to the applications.

Where things begin to break down is when we start studying non-linear equations and systems during the remaining of the year. This will include quadratic, cubic (and some higher order polynomials), logarithmic, exponential, and trigonometric functions. There are more parameters in these equations, the graphs are more challenging to generate. We will spend time reviewing the basics concepts of functions in general: domain, range, and different ways to express functions. There are also issues with symmetry which need to be addressed: with respect to the x-axis, y-axis, and the origin.

The key issue which I hope to address as the year progresses is what the key characteristics are of each type of non-linear functions. My goals are as follows: given any equation, a student will be able to recognize what type of equation it is, sketch a basic graph of the function, and give an example of how this function is used in a useful context. What is fundamental here is the ability to represent functions in multiple ways.

I will know if students really understand the differences in these functions if they can look at a word problem, generate some data points, graph the points, and then made a prediction as to the type of function that is being represented. The final step is to use this to make predictions outside of the data set.

As I consider all the concepts that will be covered during the year, I realize that I need to be very strategic and intentional about why studying the different types of functions is so important. Each of the functions we study has distinct applications in the real world. It is important that students realize how these different functions can be used to model situations and make predictions. If the wrong model is chosen for a particular situation, it can lead to loss of time and money. In regards to urban planning, budgets will be used inappropriately or there may even be a shortfall. Significant time will be wasted (too many schools built or not enough). I often use the following situation in my class. Suppose you are working for the city of Chicago and are asked to look ten years into the future to plan for the number of neighborhood schools necessary. You are given five or six data points and need to predict future enrollment in high schools. Will you use a linear model? Quadratic? Exponential? Depending on the one you chose has huge implications for budgeting, assessment of taxes, and urban planning in general. To model situations appropriately using existing data is of extreme importance.

2. Determine acceptable evidence (performance of understanding)

When presenting a new concept, I have students write on individual whiteboards so I can give immediate feedback and check for understanding. I use exit slips in order to plan the next lesson. I usually assign homework four nights each week. I vary homework with classwork that needs to be turned in at the end of the period and I have quizzes every other week.

In the video I made this summer, I used LEGOS to build a parabola and show some its key characteristics. This is one of the things I will ask my students to do: create a short video showing key characteristics of the type of function we have studied. I hope the students will use simple props, each other, and things that they can find around the house. As in my video, I started with very traditional types of questions for a test. I then constructed a parabola showing its vertex, axis of symmetry, and its failing of the horizontal line test. I ended with the application of parabolas: their necessity in designing headlights (also used for satellite dishes).

I will have students keep track of key concepts in a particular unit. Not all of the concepts will need to be included in the short videos but when I design the rubric for grading the videos, I will have a spot for them to list the concepts they will include. This will help them be more organized in the production and will make it easier to grade with consistency. Most of my students have smart phones and I hope they will be able to make their videos with those, or borrow one from a friend. If the students do group videos, I am sure they will have access to the necessary technology. As I did in my video, I want the students to be sure to give a practical application for the concepts we have learned.

Alternative assessments are the focus of my Deep Play Group. It was fascinating for me to make the video – it caused me to reflect on key concepts of a parabola, it had to be do-able, I had to present it, and I had to be creative. I have no doubts that my students will thoroughly enjoy doing these projects and presenting them to the class. I hope by the end of the year, I will have a number of short videos for each concept. My plan is for students to choose one particular concept to focus on. They may do more for extra credit.

As we move through the year, students can choose from functions that are quadratic (paths of projectiles), logarithmic (applications in sound), exponential (application in population growth, growth in the value of stocks, depreciation of cars), and trigonometric (% illumination of the moon, temperature changes through seasons). The possibilities are endless. I will have to have traditional tests and quizzes but I will shift my focus to these opportunities for presentation in video format.

3. Plan learning experience and instruction.

Some of our incoming freshmen at Von Steuben already will have credit in Algebra 1. We do, however, have most of our freshman class taking Algebra 1 for the first time. Many districts offer pre-algebra to freshmen or double-period Algebra 1. CPS does not offer pre-algebra as a class and although we offered double-period years ago, it is not currently offered.

In CPS, there is a required sequence of Algebra 1, Geometry, and Advanced Algebra in order to receive a high school diploma. Many of the topics we study in Advanced Algebra are ones from Algebra 1, just studied in greater depth and to revisit to ensure mastery. Now with Common Core, we are increasing the number of concepts covered and this is a delicate situation for many students who struggle in math. I state this so that if some of the concepts I mentioned are viewed as traditionally taught in Algebra 1, you will know the context.

This will be the beginning of my 29th year of teaching. I taught physics for 5 years at Fenwick High School in Oak Park, Illinois before coming to Von Steuben. I have only taught mathematics at Von Steuben and as I mentioned earlier, I have taught Double-Period Algebra 1 up through AP Calculus. I have been the chair of the department for fifteen years.

Because of my background in physics (minor from North Park University), I have found that it has given me a more broad foundation for the application of math. Each year, I do class activities that I used to do in physics, varying the desired outcomes: sometimes more on the regression analysis using graphs to produce an equation, other times using data to show specifically how an equation models a real life situation (ball bouncing to half its original height as in a geometric sequence). Many of the students taking Advanced Algebra will also be taking physics. This allows for great cross-curricular instruction. I know all three physics teachers very well.

The Advanced Algebra students will be predominantly JRs but there will be some sophomores who came to Von with Algebra credit and took Geometry as a freshman. Many of the JRs may have had difficulty with Algebra 1 and Geometry. The fact that it is a graduation requirement can be good and bad: some feel it is a necessary evil, just focusing on getting through it, doing whatever is necessary, just passing the class. The positive side is that since they need it to graduate, they will usually put forth the effort. I really enjoy teaching JRs and often it is the case that I had them as freshmen two years earlier.

I have adequate access to technology. I have never felt restricted in my instruction due to the lack of technology. I have a classroom set of chromebooks I can use, a classroom set of graphing calculators, and I use a tablet on a daily basis to guide/scaffold my lessons, and of course many students now have phones to access the internet in class. Our school just purchased new projectors from Hitachi which can interact with any white board, using it essentially as a SMART board. Our principal is very supportive in new initiatives and I hope I will be able to purchase slates for students to be able to interact with the white board from their seats in addition to coming to the board. I was the first in our department to get a tablet eight years ago. I was able to persuade our principal to invest in them for all our department members. It has been a great opportunity for collaboration – we share lessons and files on a daily basis. I am looking forward to sharing the things I learned this summer and it will be great to have Tim Nuttle to bounce ideas off as we move through the year. There are 12 teachers in the department which is a good size. There are approximately 1650 students at Von Steuben.

As I stated in my I-Video, I will plan on students Diving deep into math content, Climbing up (basically students constructing/reconstructing the concepts for themselves), then SHARING what they have learned with me and their peers. I believe I have developed well scaffolded instruction techniques over the years which I will continue with this year. I would like to have students journal more (long term) but I plan to use exit slips on a regular basis to check for understanding to guide instruction for the next day. I frequently use small white boards in class to get immediate work/feedback from students. As I learned in a PD session years ago, what I tell them is not nearly important as what they tell me.

When I met with my principal this week, I discussed with her the overlapping circles of pedagogy, technology, and content. I feel I have a very good grasp of content (this has been frustrating over the last few years as CPS changes focus and Common Core has come into existence) and good ways to use technology to teach concepts. Where I am going to really focus this year is on my pedagogy: really working on the BEST methods for increasing enduring understanding. As I said earlier about my I-Video, I used simple things such as LEGOS to show important concepts. I spent MANY hours working on the video but it was very enjoyable time spent. My hope is that my students will feel the same way – it won’t feel as though they are using countless hours doing meaningless homework but instead will enjoy producing something which they can present to their peers.

Although I will focus predominantly on videos which show enduring understanding, I will also try to have students make short videos focusing on common misconceptions. This will be secondary to what I hope to achieve but should take shape as the year progresses. I hope students will be able to look back at previous topics and explain/share what things were difficult at first but now make sense.

1. Identify Desired Results:

From what we studied this summer, I realize I need to shift much more of my teaching to showing the applications of the concepts we are studying, especially with the Advanced Algebra students. Many of the students in Advanced Algebra will have shown signs of struggling in Algebra and/or Geometry. Many of them do not feel math is their best subject or even one they care to study. Since many of their classmates from FR and SO year have chosen to take Honors Advanced Algebra, their feelings are reinforced that they can’t do math. I have taught all levels of courses from Double-Period Algebra 1 to AP Calculus. I enjoy teaching AP Calculus because of the deep level of mathematics. I have always enjoyed mathematics because of its beauty and elegance, the way concepts overlap and fit together. I realize not all of my students share this same love for math and need to focus on the “usefulness” of mathematics, the importance of its application. Really being able to answer “When am I ever going to use this??!!”.

The focus in most Algebra 1 courses is order of operations, operations with signed numbers, simplifying and evaluating expressions, solving linear equations, and usually ending the year with solving quadratic equations. The focus changes slightly from school to school, depending on how much pre-algebra is offered at the lower grades.

In my Advanced Algebra course, I will be beginning the year with a review of linear equations. We will spend time graphing lines, analyzing slope, drawing lines of best fit, and focusing on the applications of linear equations. Most applications involve phone plans, car rentals, prices for parking, and distance/rate problems. Most students are fairly comfortable with these scenarios since there are few parameters in the equations and they can easily relate to the applications.

Where things begin to break down is when we start studying non-linear equations and systems during the remaining of the year. This will include quadratic, cubic (and some higher order polynomials), logarithmic, exponential, and trigonometric functions. There are more parameters in these equations, the graphs are more challenging to generate. We will spend time reviewing the basics concepts of functions in general: domain, range, and different ways to express functions. There are also issues with symmetry which need to be addressed: with respect to the x-axis, y-axis, and the origin.

The key issue which I hope to address as the year progresses is what the key characteristics are of each type of non-linear functions. My goals are as follows: given any equation, a student will be able to recognize what type of equation it is, sketch a basic graph of the function, and give an example of how this function is used in a useful context. What is fundamental here is the ability to represent functions in multiple ways.

I will know if students really understand the differences in these functions if they can look at a word problem, generate some data points, graph the points, and then made a prediction as to the type of function that is being represented. The final step is to use this to make predictions outside of the data set.

As I consider all the concepts that will be covered during the year, I realize that I need to be very strategic and intentional about why studying the different types of functions is so important. Each of the functions we study has distinct applications in the real world. It is important that students realize how these different functions can be used to model situations and make predictions. If the wrong model is chosen for a particular situation, it can lead to loss of time and money. In regards to urban planning, budgets will be used inappropriately or there may even be a shortfall. Significant time will be wasted (too many schools built or not enough). I often use the following situation in my class. Suppose you are working for the city of Chicago and are asked to look ten years into the future to plan for the number of neighborhood schools necessary. You are given five or six data points and need to predict future enrollment in high schools. Will you use a linear model? Quadratic? Exponential? Depending on the one you chose has huge implications for budgeting, assessment of taxes, and urban planning in general. To model situations appropriately using existing data is of extreme importance.

2. Determine acceptable evidence (performance of understanding)

When presenting a new concept, I have students write on individual whiteboards so I can give immediate feedback and check for understanding. I use exit slips in order to plan the next lesson. I usually assign homework four nights each week. I vary homework with classwork that needs to be turned in at the end of the period and I have quizzes every other week.

In the video I made this summer, I used LEGOS to build a parabola and show some its key characteristics. This is one of the things I will ask my students to do: create a short video showing key characteristics of the type of function we have studied. I hope the students will use simple props, each other, and things that they can find around the house. As in my video, I started with very traditional types of questions for a test. I then constructed a parabola showing its vertex, axis of symmetry, and its failing of the horizontal line test. I ended with the application of parabolas: their necessity in designing headlights (also used for satellite dishes).

I will have students keep track of key concepts in a particular unit. Not all of the concepts will need to be included in the short videos but when I design the rubric for grading the videos, I will have a spot for them to list the concepts they will include. This will help them be more organized in the production and will make it easier to grade with consistency. Most of my students have smart phones and I hope they will be able to make their videos with those, or borrow one from a friend. If the students do group videos, I am sure they will have access to the necessary technology. As I did in my video, I want the students to be sure to give a practical application for the concepts we have learned.

Alternative assessments are the focus of my Deep Play Group. It was fascinating for me to make the video – it caused me to reflect on key concepts of a parabola, it had to be do-able, I had to present it, and I had to be creative. I have no doubts that my students will thoroughly enjoy doing these projects and presenting them to the class. I hope by the end of the year, I will have a number of short videos for each concept. My plan is for students to choose one particular concept to focus on. They may do more for extra credit.

As we move through the year, students can choose from functions that are quadratic (paths of projectiles), logarithmic (applications in sound), exponential (application in population growth, growth in the value of stocks, depreciation of cars), and trigonometric (% illumination of the moon, temperature changes through seasons). The possibilities are endless. I will have to have traditional tests and quizzes but I will shift my focus to these opportunities for presentation in video format.

3. Plan learning experience and instruction.

Some of our incoming freshmen at Von Steuben already will have credit in Algebra 1. We do, however, have most of our freshman class taking Algebra 1 for the first time. Many districts offer pre-algebra to freshmen or double-period Algebra 1. CPS does not offer pre-algebra as a class and although we offered double-period years ago, it is not currently offered.

In CPS, there is a required sequence of Algebra 1, Geometry, and Advanced Algebra in order to receive a high school diploma. Many of the topics we study in Advanced Algebra are ones from Algebra 1, just studied in greater depth and to revisit to ensure mastery. Now with Common Core, we are increasing the number of concepts covered and this is a delicate situation for many students who struggle in math. I state this so that if some of the concepts I mentioned are viewed as traditionally taught in Algebra 1, you will know the context.

This will be the beginning of my 29th year of teaching. I taught physics for 5 years at Fenwick High School in Oak Park, Illinois before coming to Von Steuben. I have only taught mathematics at Von Steuben and as I mentioned earlier, I have taught Double-Period Algebra 1 up through AP Calculus. I have been the chair of the department for fifteen years.

Because of my background in physics (minor from North Park University), I have found that it has given me a more broad foundation for the application of math. Each year, I do class activities that I used to do in physics, varying the desired outcomes: sometimes more on the regression analysis using graphs to produce an equation, other times using data to show specifically how an equation models a real life situation (ball bouncing to half its original height as in a geometric sequence). Many of the students taking Advanced Algebra will also be taking physics. This allows for great cross-curricular instruction. I know all three physics teachers very well.

The Advanced Algebra students will be predominantly JRs but there will be some sophomores who came to Von with Algebra credit and took Geometry as a freshman. Many of the JRs may have had difficulty with Algebra 1 and Geometry. The fact that it is a graduation requirement can be good and bad: some feel it is a necessary evil, just focusing on getting through it, doing whatever is necessary, just passing the class. The positive side is that since they need it to graduate, they will usually put forth the effort. I really enjoy teaching JRs and often it is the case that I had them as freshmen two years earlier.

I have adequate access to technology. I have never felt restricted in my instruction due to the lack of technology. I have a classroom set of chromebooks I can use, a classroom set of graphing calculators, and I use a tablet on a daily basis to guide/scaffold my lessons, and of course many students now have phones to access the internet in class. Our school just purchased new projectors from Hitachi which can interact with any white board, using it essentially as a SMART board. Our principal is very supportive in new initiatives and I hope I will be able to purchase slates for students to be able to interact with the white board from their seats in addition to coming to the board. I was the first in our department to get a tablet eight years ago. I was able to persuade our principal to invest in them for all our department members. It has been a great opportunity for collaboration – we share lessons and files on a daily basis. I am looking forward to sharing the things I learned this summer and it will be great to have Tim Nuttle to bounce ideas off as we move through the year. There are 12 teachers in the department which is a good size. There are approximately 1650 students at Von Steuben.

As I stated in my I-Video, I will plan on students Diving deep into math content, Climbing up (basically students constructing/reconstructing the concepts for themselves), then SHARING what they have learned with me and their peers. I believe I have developed well scaffolded instruction techniques over the years which I will continue with this year. I would like to have students journal more (long term) but I plan to use exit slips on a regular basis to check for understanding to guide instruction for the next day. I frequently use small white boards in class to get immediate work/feedback from students. As I learned in a PD session years ago, what I tell them is not nearly important as what they tell me.

When I met with my principal this week, I discussed with her the overlapping circles of pedagogy, technology, and content. I feel I have a very good grasp of content (this has been frustrating over the last few years as CPS changes focus and Common Core has come into existence) and good ways to use technology to teach concepts. Where I am going to really focus this year is on my pedagogy: really working on the BEST methods for increasing enduring understanding. As I said earlier about my I-Video, I used simple things such as LEGOS to show important concepts. I spent MANY hours working on the video but it was very enjoyable time spent. My hope is that my students will feel the same way – it won’t feel as though they are using countless hours doing meaningless homework but instead will enjoy producing something which they can present to their peers.

Although I will focus predominantly on videos which show enduring understanding, I will also try to have students make short videos focusing on common misconceptions. This will be secondary to what I hope to achieve but should take shape as the year progresses. I hope students will be able to look back at previous topics and explain/share what things were difficult at first but now make sense.

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