Scatter Plot Lesson Plan

Purpose: This lesson is designed for 8th grade students to explore scatter plots.

Prior to the lesson have students work in groups 4 to collect data on 20 people on one of the following topics: number of hours people work and their salaries, amount of hours high students study and their GPA, student’s arm span and their heights.

Give students a worksheet of a scatter plot about the population growth from 2000-2004,  have the students answer the following questions.

What was Washington’s percentage growth from 2000 to 2004? _________

What other information can be given for point labeled Washington? _________

Which state had the largest population growth by July of 2004? _________

What information can be given from a data point? _____________________________________

______________________________________________________________________________________________________________________________________________________________

___________________________________________________________________________________________

Write a statement about North Dakota? ____________________________________________

_________________________________________________________________________

Discuss the responses with the students. Discuss and explain the following term using the scatter plot above: data point, scatter plot, cluster, outlier.

Explain to the students that they will be creating scatter plots using the information they collected from the survey they completed with their group. Have the students use the Excel application on their computers to enter the information they collected from their survey. Guide students through creating a scatter plot in Excel.

Discuss with students how a scatter plot shows a relationship between two sets of data. Have students identify the outliers, and the clusters with the scatter plot. Next have the students write a brief statement about the data based on the scatter plot.

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Assessments

A Look At Assessments

Assessment is an on-going process aimed at providing insight and improving student learning. It involves making expectations clear to students and setting outcomes for learning. It used as an indicator on how well student performance matches those outcomes. It uses the resulting information to improve student learning. The assessment process helps to support academic culture dedicated to assuring and improving student learning. Assessment of student learning occurs at various academic levels. http://www.oaklandcc.edu/assessment/Definition.htm

In the educational world data drives instruction, educators are constantly collecting data about their students in the form of assessments. Assessments provide educators with vital information that determine instructional strategies, interventions, student placements, IEP goal, and school wide plan.

It’s important that assessment occurs in order students to be provided with the instructional supports necessary for them to be successful. Through this assignment I realized that assessment examples overlap assessment categories. Educational Leadership indicates that formative and summative assessments are sometimes because of the intended purpose of the assessment. To learn more about the assessment see the chart below.

As a teacher who likes to use creative ways to assess students I find it difficult to say I like an assessment over another because I assess based on student’s abilities, needs, and IEP goals. Like most educators, my concern, I have to be very careful not to run into the trap of teaching to a test. No Child Left Behind and the push to make AYP sometimes limit the assessments used in schools. As a teacher in a district with a scripted curriculum and the types of assessments dictated it’s sometimes difficult to use meaningful assessments.

Type of Assessment Examples
Formative Assessment-

  • Occurs during the instructional process and provides information that teachers use to adjust learning and teaching in order too ensure students are making strides toward achievement for the targeted standard based learning goals.
  • Helps teachers determine the next steps during the next steps during the learning process
  • Students should be active participants as a means of promoting student involvement and student achievement.
  • Criteria and goal setting
  • Observations
  • Questioning Strategies
  • Self Assessments and Peer Assessments
  • Student Record Keeping
Summative Assessment–

  • Given periodically to determine what students know.
  • Serves as a tool to help evaluate the effectiveness of programs, school improvement goals in alignment to school curriculum or student placement in specific programs.
  • Cannot be used at a classroom level to make immediate instructional adjustments or provide intervention because they occur well after instruction has been given.
  • Data from summative assessments are also for school accountability AYP.
  • State assessments
  • District Benchmarks or Interim Assessments
  • End-of-Unit or Chapter Test
  • End of Term or Semester Exams
Objective Assessment –

  • Based on all the students learning the same things
  • Have a true answer
  • Multiple Choice
  • True False
  • Short Answers
Subjective Assessment –

  • Based on teacher’s judgment to determine the grade
  • Takes longer to grade
  • Consist of complexed questions
  • Essay type questions
Self-Assessment –

  • Informs the learner
  • Encourages independent learners
  • Can increase student motivation
  • Help students check if they mastered a topic, skill or concept
  • Peer Review
  • Practice Quiz
  • Games
  • Interactive Activities
Peer Assessment –

  • Students evaluate each other
  • Critique each others work
  • Rubrics
  • Checklists
  • Feedback Diagrams
Authentic Assessment –

  • Reflect real-world situations
  • Consist of topics and issues that interest students
  • Students produce a quality product or performance
  • Students are aware of the evaluation criteria and standards
  • Allows for self-evaluation and self-correction
  • Portfolios
  • Constructed Responses
  • Self Assessments
  • Observations
  • Projects
  • Exhibitions
  • Rubrics
Constructed Responses –

  • Students apply knowledge, skills, and critical-thinking abilities to real-world, standards-driven performance task
  • Students construct their own answers
  • Teachers use the information to gauge students’ understanding of skills such as graphing, measuring, sorting etc..
  • Prompts
  • Short Answers
  • Showing Work
  • Visual Depiction Activities
Selected Responses –

  • Students are provided with response to choose from
  • Multiple Choice
  • True/False
  • Matching
  • Fill in the Blanks
Standardized Assessments –

  • Predetermined criteria
  • Administration and scoring are in consistent manner
  • PSSA Assessment
  • SAT’s
Performance Assessment –

  • Students demonstrate something that meets a specific criteria
  • Research Papers
  • Create Math Models
  • Producing a Book
  • Exhibits
  • Culminating Activities
Ability Assessments –

  • Designed to assess a student’s ability to complete certain task
  • Results from the assessment determines placement into programs
  • Provides teachers with information about deficits with skills to be addressed through intervention
  • Assess student’s readiness
  • Woodcook-Johnson III
  • Iowa Algebra Aptitude Test
  • Cognitive Abilities Test

Resources

http://www.nmsa.org/Publications/WebExclusive/Assessment/tabid/1120/Default.aspx

http://vudat.msu.edu/subjective_assess/

http://www.rapidresources.com/res_const_response.asp

http://jonathan.mueller.faculty.noctrl.edu/toolbox/tasks.htm

http://www.rmcdenver.com/useguide/assessme/online.htm

http://www.riversidepublishing.com/products/wjIIIComplete/index.html

Live Event Reflection

#mathchat Thursday @ 7:30 – How do we assess whether or not mathematical concepts have been grasped and understood?

This topic aligned with Task 5-4 on assessment. The discussion started out with examples of assessment such as journals, sticky notes, observations, formative and summative assessments. To assess understanding during instruction red and green cups is an excellent idea or just have a conversation with the students. There was a consensus that assessment is a vital part of instruction and should occur often. We discussed how to assess whether students just understood a concept of if they  apply the concept. Suggestions for assessing student’s understanding included having students recall facts or use a formula, and for assessing student’s ability to apply a concept they could complete a project.

Toward the end of the chat a question about what do we do with the information gathered after an assessment. Suggestions included proving students with feedback and using the information to re-teach.

Assessment is indeed a vital part of the learning process and teachers should have a toolbox of assessment strategies and an idea of what to do with the information they receive after assessing students. I think teachers need more professional development on the steps to take after assessing students in math.

As usual it was an excellent and informative live chat.

Data Visualization Tools

Since I will be supporting teachers on interpreting data I decided to present  5 data visualization tools that could be useful to  teachers when sharing information based on data or when planning for their students.

Click on the image to learn more

Misleading Graphs Lesson Plan Critique

Lesson Overview

Title: Misleading Graphs Are Da’PITS!

This lessons was designed to have students use technology and websites to discover the 5 components that a graph may contain to make the information accurate.

Cartoon 1

Cartoon 2

Students are to discuss the joke in both cartoons which depicted misleading and confusing information about data representations. Next the students engage in a discussion about the differences in two bar graphs using a bar graph worksheet. Students are then introduced to an acronym they could use to help them remember the components of  a graph that must be included in order for information in the graph to be displayed accurately. Acronym – DaPITS. D-Data, P-bars in the proper proportion, I-interval, T-title/labels,and S-scale. Student are to work in groups and use the acronym DaPITS to discuss why the graph provided by the teachers contains misleading information. This lesson plan also included extension activities and other resources about about misleading graphs.

This was a well-organized lesson that used interactive activities so that students could discover how to display data accurately. The use of acronyms is an excellent tool teachers can use to help their students remember key components of a lesson or the steps to solving a problem. By using discussion as a way to have the students figure out the misleading information, the teacher is using the analysis and evaluation levels of Bloom’s Taxonomy. Another extension to this lesson, give students several examples of misleading data and have them draw conclusions about which audience the data might have been designed for or which set of data appeals to them and why..  It’s important that our students are aware of misleading data and representations because they are one of the larger groups of consumers. With that being said , real life and relevent data should be used.

Lesson Plan: http://alex.state.al.us/lesson_view.php?id=26406

Cartoon #1: http://smallbiztrends.com/2008/09/instantly-improve-your-sales-numbers.html

Cartoon #2: http://geogontobetterthings.wordpress.com/2008/06/08/data-presentation/

Symmetry: Lesson Critique

Symmetry Lesson Plan

Above is the link to a webquest lesson plan on symmetry. The lesson uses a PowerPoint as on of the task which student will undertake as they learn about symmetry. There links to websites on how to create a snowflake.I Liked the idea of using a webquest to engage students in a lesson about symmetry, however this webquest did indicate the age level the lesson was designed for. The activities were designed for the students to create snowflakes and quilt designs but did not provide guiding questions for students to discover the true meaning of symmetry.

To enhance this lesson I would include more investigative questions.

When looking for a  lesson plan on symmetry I surprised to find that there’s a limited amount of symmetry lesson plans for high school students.

van Hiele Model

The van Hiele Model is a model for how geometry curriculums should be designed. Based on this model students’ understanding of geometry is dependent on what they were previously taught.

There are four characteristics of these levels of thought:

  • The Van Hiele levels of geometric reasoning are sequential. Students must pass through all prior levels to arrive at any specific level.
  • These levels are not age-dependent in the way Piaget described development.
  • Geometric experiences have the greatest influence on advancement through the levels.
  • Instruction and language at a level higher than the level of the student may inhibit learning.

The levels are as follows:

Visualization – Students recognize and sort shapes and objects

Analysis – Students identify the properties of shapes

Informal Deduction – Students recognize the relationships between and among shapes

Deduction – Students are able to construct proofs using postulates or axioms and definitions

Rigor – Students begin to work with different geometric or axiomatic systems

It’s suggested that in elementary school geometry be taught informally through exploration and hands-on activities. It’s also possible to have students at different levels with in the same classroom as a result teachers have to differentiate their instruction.

As an elementary school teacher, I’ve observed that most students complete the visualization level and part of the analysis level. By the time the get to middle school they can identify the shapes, use the appropriate vocabulary, and identity the properties of the square, rectangle and triangle. They have difficulty with describing and explaining the relationships between and among shapes. After reading about the van Heile Model I started to think about the causes for students who aren’t advancing to the other levels on based on the van Heile Model. In think that after students have been exposed to the basic knowledge of geometry there isn’t a great emphasis on geometry in elementary school. Besides students also coming from different backgrounds and having different experiences which impact their knowledge of geometry, there’s a great emphasis of number sense in elementary schools as students are being prepared for the standardized assessments like the PSSA’s.

http://images.rbs.org/cognitive/van_hiele.shtml

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