Mathematics Updates
November 2016
Technology Enhanced Items Included on Georgia Milestones Assessment System
The state is including two-part items on the Georgia Milestones mathematics assessments this year. These items are being referred to as "technology enhanced" although they are completely functional on the pencil-and-paper version.
The items are a combination of multiple choice or multiple select, A multiple select item will allow for more than one correct answer out of the five or six options listed. The item stem will indicate how many correct responses there are. Students can earn two points for identifying all of the correct responses or one point for specific combination(s). No points are given if a student chooses all answer options.
"Technology enhanced" two-part items can contain both parts of the same type or they can be different types. For example, each part can be multiple choice, each part can be multiple select, or one part can be multiple choice and the other multiple select. Students receives one point for each part answered correctly.
Although there may be more than one "technology enhanced" items on the Milestones math assessment, only one of the items will be operational. The rest will be field test items. The change will affect the number of items on the assessment, but it will not change the number of points for the assessment.
Two examples of these new item types provided by the Georgia Department of Education Assessment and Accountability division are shown below.
Calculators are essential technology tools for teaching and learning mathematics effectively. Used purposefully, they can extend the math being taught and enhance student learning.
September Survey Results Informs State Focus for Math Professional Learning
More than 4,000 mathematics educators in the state responded to the survey which was made available in September to determine where professional learning provided by the state's Mathematics Program should focus.
The survey results identified five challenging math content standards at each grade level or course. The state is in the process of producing videos for each of these standards to illustrate what teaching and learning looks like in effective classrooms. The target date for having these videos available is July 1, 2017.
Five "Key Strategies" for Effective Formative Assessment
Dylan Wiliam, a renowned researcher on formative assessment, has written a research brief for the National Council of Teachers of Mathematics (NCTM) on the topic. He and fellow researcher Marnie Thompson have identified five "key strategies" for effective formative assessment. Effective formative assessment and synopses of the strategies are provided below. Read the entire research brief by clicking here.
Effective formative assessment
Goals for learning and criteria for success
Effective discussions, activities, tasks
Forward-moving feedback
Ownership of learning
Peers as learning resources
Open-middle problems are a little different. Like open-ended problems, they start with a closed beginning, but they also have a "closed ending" because they end with the same answer. What is interesting about open-middle problems is that path from beginning to end is not prescribed by a set of procedures. Instead, there are multiple ways to approach and solve these types of problems.
Based on Dan Meyer's idea, a website was created by Nanette Johnson, Robert Kaplinsky, Bryan Anderson, and Dan Luevanos for the purpose of collecting open middle problems. Math teachers have contributed a wealth of these items from kindergarten through high school. Items are sorted by domain within each grade level. The items may look deceptively simple, but they actually require a higher depth of knowledge than most problems, and they provide opportunities for students to problem solve and discuss their thinking.
These problems make great warm-ups or problems of the day/week. A screenshot of an example problem. written by Kaplinsky and aligned to 6.EE.7 with a DOK 3 level, is shown below. Check out the Open Middle website and begin using it with your students.
Automatically Create QR Codes in Google Sheets
I turned a practice set of solving one-variable equations into self-checking practice in just a few minutes following these steps.
Setting up the sheet:
- Go to Google drive and create a new spreadsheet.
- Label Column A "#".
- Label Column B "Directions" and include directions. Use the wrap text button to allow all the directions to be seen.
- Label Column C "Answers".
- Label Column D "QR Code".
- You can use other formatting options to center your labels horizontally and/or vertically and make them bold.
- Resize the columns and rows so they look like the screenshot below.
- Type in problem numbers in Column A, type in problems in Column B, and type in the corresponding answers Column C.
- In cell D2, copy and paste this formula: =image("https://chart.googleapis.com/chart?chs=150x150&cht=qr&chl="&C2) (You will need the entire formula shown in bold, not just the hyperlinked part. I tried unsuccessfully to remove the hyperlink. Many thanks to Tammy Worcester Tang for the formula!)
- Press the Enter key on your keyboard and the QR code will appear.
- Click once on cell D2 to select the cell.
- Click the tiny square in the bottom right corner of the cell and drag down to fill in the formula in as many cells in Column D as problems.
- Resize the rows and columns to resize the QR codes and to make the sheet more student friendly.
- Give your sheet a title.
- Printed copies of the work should not include the answers, but the answers are necessary to create QR codes that will allows students to self-check. Sooooo, select Column C by clicking in the column header labeled C.
- Change the text color to white.
The formula used to generate a QR code for cell D2 referenced cell C2, which is where the answer was located. If you set up your Google sheet where another cell contains the item you want changed to a QR code, change the third- and second-from-last characters in the formula to indicate that location. For example, if cell B2 contains the answer, the last three characters in the formula should be B2) rather than C2).
You can insert images or URLs in the column where I put answers. This idea can be adapted to lots of other activities using QR codes. The great thing about it is that you will be able to generate lots of QR codes just by clicking and dragging once you have the formula in place.
Teaching Math with a Growth Mindset
No one is born with a “math brain” while others are not. Research has disproved the "math brain" myth but it persistently believed by students and parents. Communicating to students "growth mindset" messages is critical. Because the brain has amazing plasticity, everyone is a "math person".
Carole Dweck and Jo Boaler, professors at Stanford University, have done a tremendous amount of research in the area of growth mindset. Dr. Dweck pioneered the work, and Dr. Boaler has extended it specifically to mathematics.
Math Professional Learning Opportunities
Nov. 1, 2016 - Werz Central Office, PLC - 3:30pm - 4:30pm
Coweta Elementary Mathematics Initiative Information Session
Teachers who applied to be part of the Coweta Elementary Mathematics Initiative (CEMI) should plan to attend this informational session about the program.
Nov. 9, 2016 - Northgate High School
Integrating Chromebooks into Math Teaching and Learning
A variety of ways to integrate Chromebooks into high school mathematics teaching and learning will be explored in this session. Although participation in the face-to-face sessions is limited to Northgate High School math teachers, resources will be made available through the High School Math Google classroom after the presentation.
Nov. 10, 2016 - Western Elementary School
Developing Understanding of the Standards for Proficiency and More
This session is part of a monthly series of professional learning. It will focus on diving deep into the current and/or upcoming content standards by examining aligned assessment items and engaging in tasks that will help students construct conceptual and procedural understanding. Although participation in the face-to-face sessions is limited to Western Elementary teachers, resources will be made available to all Coweta teachers through the K-2 Math and 3-5 Math Google classrooms after the presentations.
Nov. 15, 2016 - K-2 Math Webinar - 2:50pm - 3:50pm
Developing Number Concepts: Addition and Subtraction (Part I)
This is the first of a three-part series of sessions. A variety of teacher-directed and independent activities focused on helping children interpret and symbolize addition and subtraction will be discussed in this session designed for teachers of Kindergarten through Grade 2. Register by 4 p.m. on Nov. 14 at https://goo.gl/forms/96pBEBAzOuTl7WJ42 to receive an invitation to join this session.
Nov. 17, 2016 - 3-5 Math Webinar - 2:50pm - 3:50pm
Fractions and Decimals (Part II)
In this second of a series of sessions, a collection of high-leverage tasks to assist in building conceptual understanding of operations with fractions and decimals will be examined. This session is designed for teachers in Grades 3-5. Register by 4 p.m. on Nov. 16 at https://goo.gl/forms/X73pyiSWLoHcc0Br1 to receive an invitation to join this session.
Nov. 29, 2016 - Evans Middle School - 4:00pm - 5:00pm
Differentiation in Middle School Mathematics
Enishea Loggins will lead participants in a session focusing on differentiation in middle school mathematics. Participants are asked to bring their Chromebooks. No registration is required.
Research base
Blackwell, L.S., Trzesniewski, K.H., & Dweck, C.S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246-263. Retrieved from http://mtoliveboe.org/cmsAdmin/uploads/blackwell-theories-of-intelligence-child-dev-2007.pdf
Fincher, M. (2016, September). Fall 2016 GACIS Georgia Milestones update. Georgia Department of Education. Retrieved from http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/default.aspx
Johnson, N., Kaplinsky, R., Anderson, B., & Luevanos, D. (n.d.). Open middle: Challenging math problems worth solving. Website URL http://www.openmiddle.com/
Kline, B. (2016, October 19). Fall 2016 GCSM Mathematics Program update. Presentation to the Annual Fall Conference of Georgia Council of Supervisors of Mathematics, Madison, GA.
Mindset Works. (n.d.). Teacher practices. Website URL https://www.mindsetworks.com/science/
Tang, T.W. (2014). Batch-create QR codes in Google spreadsheet. Tammy’s Technology Tips for Teachers blog. Website URL http://tammyworcester.com/
Wiliam, D. (2007). Research brief: Five “key strategies” for effective formative assessment. Reston, VA: National Council of Teachers of Mathematics (NCTM). Retrieved from http://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Benefits-of-Formative-Assessment/