Learning Progress: Intro to Stats and Data – CCSS.Math.HS.ID

Learning Progression

HS.ID.A.1 – Represent data with plots on a real number line (dot plots, histograms, and box plots).

• Read and contextualize graphs and tables
• Analyze how data is represented (e.g. “Is this the best graph for this data?”)
• Create graphs and tables for data sets and give reasoning.

HS.ID.A.2 – Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

• Contextualize the skew of data
• Calculate interquartile ranges, standard deviation, and distribution
• Create a graph – or data set – that represents a given description

HS.ID.A.3 – Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

• Identify outliers
• Create graphs and/or tables for two data sets and compare them

Assessments:

• Student discourse
• Mathematical reasoning
• Use of visuals
• Contextualizing to personal examples/experiences
• Hinge questions

Modeling a Digital and Global Age Learning Environment

Modeling a Digital and Global age Learning Environment

Brittany Moore

Bolded words are linked to sites!

Technology is even more present in our world than ever, and a very large part of our students’ daily lives and in how they see and interpret the world around them, so it only makes sense that it is incorporated into their standard learning regimen.

Web 2.0 refers to the new stage in development in the World Wide Web that allows users to interact with webpages rather than just use them as a source of information. This is a wonderful opportunity for teachers and should be taken advantage of.

There are many new ways for teachers to connect and share ideas, which they can use to create new lessons and gain new teaching strategies or to find ideas to supplement their already tried and true methods. Teachers may also find this helpful to help students who are struggling and not grasping the concept the way the teacher is teaching it. Many teachers think of Pinterest when they think of turning to the internet to find creative lesson ideas, but would you have thought to look at Scholastic for interactive math lesson ideas? They even have some awesome tips for integrating technology into your classroom.

You have used technology find ways to enhance your lesson, now how can you present this information to your students in a way that uses the technology to make it fun and interesting? Rather than standing at the front of the room lecturing, one go to form of presentation is the Prezi, an interactive slideshow presentation that is customizable to your presentation. Now, a slideshow presentation may seem like a difficult or dull way to learn math, but this Prezi about the number system provides an amazing visual for students.

https://prezi.com/n-8ibkiw881r/number-systems/

Prezi can be accessed for free, but creating a free presentation allows Prezi to add it to their database for other users to search and view or use, which can also be a helpful way for teachers to find new ideas or ways to present topics. This could be an example to students about how to be responsible about what they post because once it’s online it stays online forever, and also to discussions about plagiarism the consequences of taking someone else’s work to pass it as your own.

Other sites that can be extremely helpful, Desmos Graphing Calculator is not only an extremely useful resource for students, it also has pre-programmed examples under the tab on the left side and allows sliders to be able to plug in variables into generalized formulas.

This could be used as a modeling exercise during instruction. A teacher could even project the graph or lines up onto the whiteboard and mark points or lines on the perfectly projected graph rather than having to draw the axis and try to guess while plotting points, this will make it easier for students to see exactly where points are. This is also a helpful resource for students when they are at home they can access the examples. Desmos is also available as an app on all devices and could be used as a support or accommodation for students who may have difficulties with fine motor function and are unable to graph on paper.

One way that utilizes technology and makes assessment fun for students is Kahoot!, a survey type quiz program that allows students to use their phones or computers to answer questions projected onto the board. Students receive points for their answers correctness and then the speed of their answer. This can be a fun formative assessment as well self assessment for teachers and students to gauge the students’ understanding of the topic and determine what materials need more focus or review.

8.EE-Modeling Activity-SMART Board: helping solve systems of equations

This modeling activity can be useful for an Algebra teacher that wants to integrate technology in the curriculum. The central focus of this modeling activity is for students to gain confidence as they learn how to manipulate linear equations into slope-intercept form in order to graph the lines and find the solution. Since the modeling class size is small, about half of the students will be able to use the SMART Board, at a time, to help them reach the learning targets. Essential questions for students to answer during this lesson include:

• What does a system of equations look like?
• How do I graph a system of equations?
• Can I graph an equation that is not in slope-intercept form?
• How can I find the solution on the graph?
• What does a written solution look like?
• When is this method best used?

Here is the detailed modeling activity plus the lesson plan :

Modeling Technology Explanation

Modeling Technology Lesson Plan

And here is a link to a video that can walk you through setting up a graph on the SMART Board:

Collaborative Mathematics Projects

A classroom math project can be come more meaningful by collaborating with classrooms all around the world through the Internet. In this blog I will suggest features that are part of good collaborative projects and some examples of ways to make math activities from existing global collaborative projects.

Features of good collaborative projects:
1. Central question engages student to think.
2. Students can share data, solutions, and strategies.
3. Students can peer assess and tutor via the internet.

Guidelines and requirements:
1. Teachers should know who and how students are collaborating.
2. Teachers must make sure that students are following district Internet policies.
3. It is easiest to use existing Internet sites.
4. Get parent permission to internet publish reports, artwork, pictures, or video.

Math activities ideas using existing global projects:

The Big Mac index was invented by The Economist in 1986 as a lighthearted guide to currencies but now it is used for much more. This index allows teachers and students to ask mathematically testable questions, such as, “In what countries could the average person work for one hour and buy a Big Mac?” Collaboration comes from reading the blog posts on The Economist website and posting a hypothesis or some analysis through the teacher.

The Down the Drain Project is a collaborative community that analyzes how much water people use everyday. This project has worksheets and guidelines that support the teaching of creating hypothesis, making predictions, analyzing data to test predictions, and write conclusions. There is a worksheet calculating daily water use and sharing the data with the collaborative project members.

Site for starting a new collaborative project:
Class2class is an Internet service where math teachers can come to join in new projects and collaborations.

Implementing Student Voice into Mathematics Teaching

Just like Performance-Expectations (PE) Student-Voice is a Washington State term that refers to teaching practices focused on the student involvement. Some of the principles of Student-Voice are: 1. Eliciting student understanding of the learning targets; 2. Supporting student use of resources to learn and monitor their own progress; and 3. Teachers reflection on Student-Voice evidence to improve instruction. Recently two mathematics masters students and Washington State teacher conducted action research projects related to Student-Voice. The reading of these action research projects will help mathematics teachers and pre-service teachers understand what Student-Voice is, why it is important, and how to implement teaching practices related to this area teaching best practices.
Emphasizing Performance Expectations to Increase Student Achievement, by Jennifer Coulson Emphasizing PE to Increase Math Achievement-Jennifer Coulson

Using Learning Targets to Encourage Student Self Assessment and Increase Student Achievement in Geometry, by Katelyn Marie Pierce UsingLearningTargets_Geometry_Pierce_project

Using Assessment Information to Plan for Next-Step Instruction

Share a plan for identifying and correcting misconceptions related to a key performance standard in one of your courses. Please share your lesson plan and then elaborate on your:
o Method of analyzing student work to identify student performance with respect to state standard (identify patterns of student errors and analyze these patterns to understand student thinking).
o Plan for next-steps support and instruction for the whole class, subgroups, and individuals. This plan must include a cycle of instruction matched with assessment for modification as the students move closer to achieving the learning target.
o Plan for student feedback so that the students can takes ownership of their achievement.

The attached document has helpful information about how to identify and interpret error patterns.Assessment and Remediation Plan

Equity issues in planning a problem solving lesson

How do you adapt problem solving lessons so that they are accessible by all the students in your classes? Include a lesson idea and a reflection explaining how your adaptation will support the diverse needs of your students.

The CRAFT framework is for making math problem solving lessons accessible and engaging for diverse classrooms. CRAFT Framework

Planning Standards-based Problem Solving Lessons

How do you create true problem solving lessons that are aligned to specific mathematical knowledge and /or skills? Include a lesson idea and a reflection explaining  how you would implement this planning idea.  A good place to start if you are a teacher in the state of Washington is http://standards.ospi.k12.wa.us/Default.aspx?subject=7,PE After you understand the learning targets of the mathematics standards you must have a good resource of problem solving activities and ideas.  Here is a good website for adapting textbook math problems to make them real problem solving activities http://www.homeschoolmath.net/teaching/problem_solving.php.

Please share with use your ideas for planning problem solving activities that are aligned to specific mathematics standards.