Math Professional Learning - Making Sense of Fractions

During club day on December 9th, all math teachers participated in professional learning on Making Fractions Make Sense for Kids.  Our learning target was: I can internalize instructional practices and resources that will help students understand fractions at a deeper level.  We read and discussed the article "10 Practical Tips for Making Fractions Come Alive and Make Sense" by Doug M. Clarke, Anne Roche, and Annie Mitchell, and participated in an activity (Fraction Fish) that can be used to build conceptual knowledge of adding and subtracting fractions.

 

10 Tips for Making Fractions Come Alive and Make Sense

(Source: 10 Practical Tips for Making Fractions Come Alive and Make Sense" 

by Doug M. Clarke, Anne Roche, and Annie Mitchell. The ten tips are listed below:

1. Give a greater emphasis to the meaning of fractions than on procedures for manipulating them.
2. Develop a generalizable rule for explaining the numerator and denominator of a fractions.

3. Emphasize that fractions are numbers, making extensive use of number lines in representing them.

4. Take opportunities early to focus on improper fractions and equivalences.

5. Provide a variety of models to represent fractions.

6. Link fractions to key benchmarks and encourage estimation. 

7. Give emphasis to fractions as division.

8. Link fractions, decimals, and percents whenever possible.

9. Take the opportunity to interview students one on one with rich tasks to gain awareness of thinking and strategies.

10. Look for examples and activities that can engage students in thinking about fractions in particular and rational number ideas in general.

Big Takeaways

• Fractions are difficult to teach and learn because of the different interpretations (constructs), representations (models), and coding conventions (5/4, 1 1/4, 1.25, etc.)
• Fractions can represent 1) Part-whole, 2) Measurement, 3) Division (3 divided by 5 is 3/5), 4) An operator (3/4 of 12), and 5) A ratio.
• Teachers have typically defined a fraction by telling students "the denominator tells you how many parts the whole has been broken into, and the numerator tells you how many of these parts to take, count, or shade in".  This works well if the fraction is between 0 and 1. The authors suggested this explanation: "In the fraction a/b, b is the name or size of the part and a is the number of parts".
• Benchmarking (comparing to 0, 1/2, or 1) should be used to estimate and compare fractions.

NCTM Regional Conference in Nashville

Several of our math teachers will be attending the National Council of Teachers of Mathematics (NCTM) Regional Conference in Nashville, November 18-20.  Trussville City Schools is sending a small group of teachers from every school.  The following teachers will be attending from Paine Elementary (grades 3-5):

• Karen Ekonen - 3rd Grade
• Rachelle Taylor - 4th Grade
• Susan Brandon - 5th Grade

Participating teachers will design future professional development for all of our math teachers based on what they learn at the conference!

Lisa Lothspeich and Jana Walls will be leading a session at the conference on Developing Multiplication Fact Fluency in the 21st Century. They will also attend sessions at the conference.

If you would like to apply to present or co-present at one of the regional conferences in the future, please get with Lisa and she can step you through the process.

Updates - Curriculum Guides, Grade Weights, Online Assessments

Grade Weights

Math Teachers met 10/21/15 to discuss, and finalize, the weights for our report card categories.  We agreed to the following:

55% - Classwork (Includes workshop, menu, and investigative tasks)
40% - Assessments (Includes mid & end of unit assessments and performance tasks)  
5% - Homework

We were comfortable increasing classwork to 55% because it is comprised of independent tasks completed in math workshop in addition to collaborative tasks (menu & investigations).  This should provide a balance in that category.

Curriculum Guide - Additional Performance Tasks

Math Teachers expressed a need for additional assessments (that can be graded) in the curriculum guides.  We discussed not wanting to spend too much instructional time on these additional assessments.  In response, we will include additional short (15 minute) performance tasks in future curriculum guides.  These will included in place of a number talk at strategic points in the unit (after a concept or skill has been taught for mastery).  We still must complete a minimum of 3 number talks per week.

Online Assessments on Achievement Series

As we continue to transition to administering our unit assessments on Achievement Series, here are a couple of things to remember:

• If you provide a paper copy, please do not have students use this in isolation, and enter their data later.  This will not prepare them for an authentic online testing experience (which they will have with ACT Aspire in the spring).
• If you provide the paper copy, please do that in addition to having them work on the computer. This should be done simultaneously, i.e., they work a problem on the paper copy, then enter the response on the computer; and then, they move on to the next problem.  This provides a better simulation of an online testing experience, and reduces the number of "data entry" errors (that commonly occur when done in isolation).

Once all students in the grade level have taken the online assessment, this data should be briefly analyzed in CAD.  CAD leaders please let me know when all tests have been administered, and I will run the grade level report and send to you.  This is a way for us to analyze the effectiveness of our unit of study.

As always, if you need any help with this please let me know.

Eureka Mini-Lessons (Key Points & Video Links)

The following are key points on how to use Eureka as the resource for our mini-lessons.

• The guided instruction component in our curriculum should be in the form of "mini" lessons not to exceed 20-30 minutes.
• These mini-lessons typically occur in our curriculum every other day.
• If your guided instruction is exceeding this time allotment, consider working fewer problems (eliminate duplicate types of problems). 
• Condense mini-lessons if you have evidence that students are already proficient with the concept or skill.
• These mini-lessons should be used to "cement" knowledge already constructed and discussed in math congress or classroom discussions.
• Allow students to use a choice of models...Eureka models are "one" tool in their toolbox.  Supporting a variety of strategies and models in considered best practice!
• Modify mini-lessons, practice sets, and homework as needed to support best practices.

The South San Francisco Unified School District has a link on their website containing tutorial videos that may be used by teachers or parents.  They are organized by grade level, with tabs for each of the modules. There are lesson videos within each module.

Please use the links below to access these videos:
3rd Grade Eureka Videos
4th Grade Eureka Videos
5th Grade Eureka Videos

Math Studio Day (GBMP)

On September 21, 2015 our math teachers participated in a Math Studio Day, a lesson study model developed by the Greater Birmingham Math Partnership (GBMP). We partnered with Faye Clark and Ann Dominick, founders of the Greater Birmingham Math Partnership initiative, to analyze cognitive demand through this model. We reviewed the factors associated with the decline and maintenance of cognitive demand.

The goals of the Math Studio Day are to: 1) Bring the math practice standards to life, 2) Increase accountability and quality of implementation, 3) Develop shared understanding of practices, 4) Deepen teacher math knowledge, 5) Foster norms and habits of instructional practice, and 6) De-privatize classrooms for professional learning and increased student achievement.

The Math Studio Protocol includes the following steps:

1. The studio teacher will discuss the lesson plans and math tasks planned.
2. All participants do the math, exploring the strategies students may use.
3. Participants anticipate the questions and misconceptions students may have.
4. Participants discuss how strategies, questions, and misconceptions may be addressed in the classroom, and how cognitive demand can be maintained.
5. Participants observe in the the studio classroom (without talking to each other or students).
6. Participants reflect on lesson objectives and level of cognitive demand.

 

A huge thank you to Jana Walls, our Math Studio Teacher for the day! Thank you for for providing us with this opportunity!

Math Data Meeting

In September 2015 math teachers met by grade level to analyze our ACT Aspire Data and baseline Global Scholar data.  We achieved growth over the previous year in all grade levels on ACT Aspire!!! In the "Ready" category, we had a high percentage of students who scored in the "Exceeds" level.  This is confirmed with our distribution of scores in our Global Scholar baseline data for this year.  This reinforces the need to differentiate instruction to meet all students' needs. Specific ideas for differentiation are included in our curriculum guides on providing additional support for students needing assistance and enrichment for students who have mastered the content.

Curriculum Guide Training

In August 2015 all math teachers (grades 3-5) participated in Curriculum Guide Training.  

Our learning targets were:

• I can describe the structure of the curriculum guides.
• I can describe the components in the curriculum guides.
• I can reason through key points that will aide me in instruction/using the guides.
• I can explain the integration of Eureka.
• I can utilize the Unit 1 guide.

We discussed how research shows the most effective instructional practices include classroom discourse and small group/one-on-one interaction with the teacher. Our curriculum provides many opportunities for peer collaboration and small group instruction with the teacher.

We discussed how Eureka math will be utilized in the form of Guided Instruction/Mini-Lessons to cement concepts after students develop conceptual knowledge through investigative tasks. 

Our curriculum is based on research-based best instructional practices. The component parts of our curriculum are shown below.  Future blog posts will highlight these components in greater detail.

Math Professional Learning - 5th Grade Algebraic Expressions & Real World Math

The teachers who attended the NCTM Regional Conference, Houston, Texas in November 2014 presented the "most impressive" things they learned during our professional learning on January 21, 2015.

Algebraic Expressions
Lisa Lothspeich shared an activity where students use a bag of M&M's to learn about variables and how to write algebraic expressions.  The following questions were posed to teachers (one by one) and we began writing expressions to identify different color groups of M&M's.

Real World Math Insights

Monica Bramlett and Lynette Summers shared some insights from a session they attended led by Dan Meyer called, "Fake World Math - Why Modeling Goes Wrong (and how to get it right)".

They shared what effective modeling looks like and two great videos from Dan Meyer.  

http://threeacts.mrmeyer.com/hotcoffee/

https://www.youtube.com/watch?v=jRMVjHjYB6w

Sources:  NCTM Regional Conference, Houston, Texas, November 19-21, 2014
Session Name:  Fake World Math: Why Modeling Goes Wrong (and how to get it right), Dan Meyer

Math Professional Learning - 4th Grade Angle Measurement & Performance Tasks

The math teachers who attended the NCTM Conference, Houston, Texas in November presented what they learned about angle measurement and performance tasks.

Angle Measurement
Rachel Davis presented a progression to help students develop a deep understanding of angles and their sizes (before ever picking up a protractor):

Angle Measurement
Rachel Davis presented a progression to help students develop a deep understanding of angles and their sizes (before ever picking up a protractor):

1) Direct Comparison - Making comparisons between different        angles.

2) Non-Standard Units - Comparing angles to standard units (pattern blocks).

3) Standard Units - Measuring with standard units (fractional parts of a circle).

Performance Tasks
Sara Wessel shared a great resource with us: Nextlesson.org.
She showed us a sample performance task from this site, which included various activities designed to differentiate.










Sources:  NCTM Regional Conference in Houston Texas, November 19-21, 2015.
Session: Angling for Understanding - Peter Stowasser, ORIGO Education
NextLesson.org

Math Professional Learning - 3rd Grade Purposeful Questioning

The math teachers who attended the NCTM Regional Conference, Houston, Texas in November presented "the most impressive" things they learned at our math professional learning on January 21, 2015.

Laney Horn and Mary Elaine Williamson presented on Purposeful Questioning.  They attended this session led by Linda Gojak, the former President of NCTM.  Posing purposeful questions is one of the 8 effective mathematics teaching practices (NCTM).  Laney and Mary Elaine showed us with how important the question prompt is when we assign a task.  We compared two different prompts:

One of the questions has students arrive at a short answer, and doesn't really tell us what they know about area/perimeter.  The second prompt tells us a great deal about the students' depth of knowledge on area/perimeter.

They also gave us a guide for "what to do" and "what NOT to do" when posing questions to students.

Source:  "Asking Questions that Promote Student Understanding" presentation by Linda Gojak, Immediate Past President of NCTM.  NCTM Houston Regional Conference 2014.