Standards and Backwards Mapping

Standards & Backwards Mapping

Introduction

When I was first introduced to the idea of backwards mapping it was through a training that my school offered on the UbD model developed by Grant Wiggons and Jay McTighe.  The presenter offered a couple poignant yet effective quotes that have really stuck with me.  The first was, "How can you give directions to a place that you don't know you are going?"  The second was clip from the children's TV show Dora the Explorer.  This clip was in every episode, and was when Dora would ask the children, "Who to we ask when we do know the way to go?"  

Most of us either had kids or had been around kids so we answered, "The Map!"  While this might seem childish and inappropriate for a teacher training, it did drive home the idea that if we truly want our kids to reach the end goal, then we must clearly know what that end goal is.

For this activity I will be focusing on my 10th grade PreCalculus class.  The standard that I will be developing my activities and assessment for comes from the common core state standards.  It is:

HSS-ID.C.7. 

Interpret the slope (rate of change) and the intercept (constant term) 

of a linear fit in the context of the data.

The reason that I chose this particular standard from the common core is because it is, for me, and many of my students the one that seems to have the most impact on how relevant math is for our everyday lives and in many of the jobs.  When I have taught them how to do this, its usefulness in the real world and the jobs that make use of this kind of work, the students are often very captivated.  The fact that it allows for the integration technology takes away some of the "math sting" that many students who dislike math or have been led to believe that they are no good at make feel.

Proficiencies for this Standard 

The proficiencies that I use to indicate what students will be able to do at the end of this unit come from the National Research Council's The Five Strands of Mathematics.  The three I would focus on here are

1. Conceptual Understanding - here the students will make the connection to what they already know (slope and constant/y-intercept) to real world applications and technology.  It done as a bi-variate statistics lesson, which I normally do, then they begin to make connections between algebra and statistics.  Tying in a concept like, say, connections, supports retention and limits errors.  By the end of the unit I would hope that the students are able to see the connection between the study of the data and the decisions that we make through the use of real life examples such as in the movie Money Ball (most of my students enjoy sports and particularly baseball).
2. Adaptive Reasoning - I would expect that after the learning experiences the students capacity to think logically, reflect on their learning, as well as to explain & justify their findings would increase.  
3. Productive Disposition - After having been through lessons and activities that were very much connected to real-life examples I would hope that the students would see mathematics as sensible, useful, and worthwhile, in addition to having developed a belief in diligence and their own efficacy.

Assessments Against the Standard

In order to measure the students achievement against the standard, I would conduct the follow formative assessments.  These three formative tasks would be part of a greater number of task that ultimately lead to a summative task for the entire unit.

1. Given several sets of data with corresponding regression (linear) equations and correlation coefficients, as well as accompanying scatter plots and lines of best fit, the students will: 
• discuss the relationship between the "closeness" of the data on the scatter plot and correlation coefficient
• interpret what the intercept (constant) means in the context of the problem
2. Given a (housing purchase) data set along with a corresponding regression (linear) equation and correlation coefficients, as well as accompanying scatter plot and line of best fit, the students then come to a conclusion as to whether it is wise to buy or sell one's home. Key to this task is for students to think logically, reflect on their learning, explain their findings, and  justify their conclusions.
3. As a reflection at the end of the unit the students would write in their ePortfolios a reflective piece on how the study of this unit has helped them to see mathematics as sensible, useful, and worthwhile.  Additionally, students would need to reflect on their own development as diligent, students who are able to produce the desired outcome.

Learning Experiences to Help Students Meet The Standard

The learning experiences for this standard would be connected to the assessments above.

1. Group work with given data sets: Given several sets of data with corresponding regression (linear) equations and correlation coefficients, as well as accompanying scatter plots and lines of best fit, the students will discuss the relationship between the "closeness" of the data on the scatter plot and correlation coefficient in their groups, coming to a consensus for presentation to the class.  Additionally, they will interpret what the intercept (constant) means in the context of the problem.  Feedback will be given to each group by the teacher and peers using a Google Form.
2. Independent work with housing purchase data: All students would be given data from different parts of the world.  Since I only have 17 students in this class, this would not be too difficult.  Each student would be responsible for coming to a conclusion based on analysis of data set along with a corresponding regression (linear) equation and correlation coefficients, as well as accompanying scatter plot and line of best fit, of whether or not it is reasonable to buy or sell a home in that region.  Their work will be presented to a partner for peer feedback (verbal).
3. Quiet reflection writing activity:  At the end of the unit the students will write a reflection on their ePortfolio addressing how the study of this unit has helped them to see mathematics as sensible, useful, and worthwhile.  Additionally, students will to reflect on their own development as diligent, students who are able to produce the desired outcome.  Only the teacher will see this and schedule one-on-one sessions with selected students to see how the lesson have done a better job meeting the above standard.

References

National Research Council. (2001). Adding it up: Helping children learn mathematics. J Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.