Planning Assessments

Introduction

For this assessment I will be focusing on my 10th grade MYP PreCalculus class who are working towards mastery of the Common Core State Standard: 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.  

This blog entry, for  the TEACH-NOW Module 5, Unit 2, Activity 2, is focused on an objective that was developed in Unit 1 - By the end of this unit, when given a set of raw data, 10th grade math students will be able to consistently represent the data as a scatter plot that is appropriately labeled and includes an appropriate scale.  (Based on the December 13 virtual class discussion, the objective was slightly modified to fit my school's context since we are an MYP school and do not use percentages).  

As a means to track student progress towards the reaching the standard, I have designed the following four formative assessments that lead to a larger, more comprehensive summative assessment:

Formative Assessment #1

The students will collect measurements of each others arm span and height.  It will be recorded and share in a single Google Spreadsheet.  The students will make a copy of the spreadsheet for their own analysis.  In their own copy of the Google Sheets the students will create a scatter plot. After successfully completing the task in Google Sheets, the students will repeat the task in MS Excel, Apple's Numbers, and their TI-nSpire graphing calculator.  For each program the students will receive verbal feedback from their peers and the teacher as to the appropriateness of the scatter plot.

Formative Assessment 2

Using the same data and scatter plot as in the first formative assessment task, the students will use the features in Google Sheets to properly label each of the axes, include a title on the graph, and a legend.   This will  be repeated in MS Excel, Apple's Numbers, and their TI-nSpire graphing calculator.  For each program the students will receive verbal feedback from their peers and the teacher as to the appropriateness of the labels, titles and legends.

Formative Assessment 3

Using the same data and scatter plot as in the second formative assessment task, the students will features in Google Sheets to create a line of best fit, linear regression equation and r-value (correlation coefficient) for the data.

Formative Assessment 4

Using the r-value from the third formative assessment task, the students will interpret the correlation of the data and how that will impact the appropriateness of the data to make predictions about the relationship between arm span and height.  This task will require no technology, however will be done in groups of three as a discussion.  Students and teachers will offer formative feedback to students in order to ensure that students are making sound, data-based predictions.

Rationale

In breaking down this larger task into smaller task, there is greater opportunity for the teacher to guide the students with formative feedback so that their end product is of high quality.  Since the summative task for this unit is for students to take a large set of raw data and carry our a regression analysis in order to make predictions and subsequent informed decisions on the loaning of money through KIVA, it is important that they are able to display the data appropriately and in a way that is not misleading.  One of the biggest areas of growth for many of the students I encounter in 10th grade is there inability to create appropriate graphs.  In having them do the regression in parts the teacher ensures that they have the right product before carrying out the next task.  In doing so, the overall product will not be impacted by a mistake in the formation stages of the product.

Since the real world uses multiple applications to do this type of work, and since our students have access to all kinds of spreadsheet programs, it is also important that they encounter a variety of applications in the formative stages of the unit.  For the summative, the students will be able to choose the application that they feel most comfortable with.  However, it is noted for the students that the TI-nSpire should be mastered as it is the only tool allowed for tests and IBDP examinations.

Finally, the fourth task is designed as a practice for the summative task, which will ask students to interpret the r-value for the KIVA data and if their predictions are sound or not.

Understanding and Applying Standards (A Reflection)

Activity 1 - Unpacking a Standard

I have had to work with the Common Core State Standards since we adopted them at my school in 2010.  Prior to that all of the schools that I worked at had not adopted any national or international standards.  After working here for the last 6+ years and completing this activity it does shock me that there are schools out there that do not have a set of standards to anchor their curriculum.  I must admit, however, that while I have worked with Common Core State Standards for the last 5 years this is the first time that I have actually taken the time to unpack them.  Unpacking the standards was an invaluable learning experience.  I actually took the time to unpack a standard that I had already worked on a couple of months ago and now find myself wanting to go back and reteach because there is so much more I could have done with it.  From the unpacking the standards activity I learned that it is effective to break the standard down into the how, the what and the why/where.  By doing this is allows me to see the standard in parts and design activities that are scaffolded to meet each part, eventually getting to the bigger picture - the context (or why/where).

Activity 2 - Backwards Mapping

While I have been using this model of unit planning since having attended UbD training in 2009, I have not resisted the trading or attended a refresher since.  Additionally I have never thought of using the concept of backwards planning in my day to day lessons, but in conducting this activity I found myself driven to implement a backwards mapping design to all of my lessons - an ambitious goal I would say.  For me, the value of backwards planning is clear.  If I, as the teacher, know the end goal of the unit (or lesson), then I know what is necessary to complete along the way to achieve that goal.  I can design all of my lessons and activities with a clear purpose.  I can offer formative feedback on the path to the goal that is specific to the big goal for the unit.  By keeping the end goal in mind, I can better deliver a quality unit of instruction and increase the probability of my students reaching the goal for the unit.

Activity 3 - Writing Objectives

It was't until I completed an activity in a previous module that I had ever thought about developing S.M.A.R.T. objectives.  I have heard of, and developed, S.M.A.R.T. goals for the math department when I was the department head, but never S.M.A.R.T. objectives for a class.  What I learned from the previous activity in another module was that actually writing S.M.A.R.T. objectives makes designing teaching & learning activities much easier!  What I learned from the activity for this module was how interdependent S.M.A.R.T. objectives and the standards are and how important it is to first unpack the standard before you develop objectives.  At the risk of sounding corny, a big take away from all three activities for me is that your objectives become smarter if you first unpack your standards and by doing do in corporation with backwards planning, your lessons are smarter and so will be your students.

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.