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.

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 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.

NCTM Regional Conference in Houston, Texas - November 2014

Eight educators at Paine Intermediate attended the NCTM Regional Conference in Houston, Texas, November 19th-21st.  We learned some new instructional approaches, strategies, tasks, games, etc, The conference also served as an affirmation of the great things we are doing in our school!  We will be sharing some of the things we learned in upcoming professional development.

Monica Bramlett, Lisa Lothspeich, Laney Horn, Rachel Davis,
Lynette Summers, Sara Wessel, Mary Elaine Williamson, & Dr. Autumm Jeter

Estimate...then Calculate

Math Practice Standard #5 includes estimation as an important skill our students should be using regularly.  “Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem.”  Students build number sense by estimating and it provides them with a way to check their answers for reasonableness (Cochran & Dugger, 2013).

The use of estimation is mentioned directly in several of our content standards.

• 3^rd Grade - Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [3-OA8]
• 4th Grade - Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  [4-OA3]
• 5th Grade - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2]

It is important that students develop the habit of estimating before calculating.  When they progress to more complex calculations such as 11.2 + 19.75 + 3, having the estimate of 33 (10 + 20 + 3) to reference will help them to quickly determine if an error was made when lining up the numbers. When students multiply and divide fractions and decimals, checking the estimate for reasonableness can eliminate many errors.   For example, in the calculation of 8.75 x 31.3, the ability to see that the answer should be around 270 (9 x 30) can help a student who may have placed the decimal point in the wrong place.  Students should even estimate when solving problems such as 7/8 x 3; 7/8 is close to a whole and 1 whole x 3 is 3.  The answer should be close to 3. 

Please continue to remind your students to estimate before they calculate, and to use the estimate to check answers for reasonableness.  If there is anything I can do to help you with this, please let me know.

Sources:

Cochran, J., & Dugger, M. H. (2013). Taking the Guesswork out of Computational Estimation. The Mathematics Educator, 60-73.

Professional Development - 10/1/14

Thank you for your participation in our professional development today.  We learned about the importance of teaching academic vocabulary (Tier II words), and the impact it will have on student achievement in all content areas.  We discovered today that math and science problems contain many Tier II words.  If students do not know these words, it may prevent them from understanding many problems.  We also talked about how often these words are used in directions provided to students.

Reminder:  A new word will be introduced each A Day by the homeroom teacher (beginning October 6th). Brief activities (1-2 minutes) will also be facilitated by the homeroom teacher on days B-H.

We are all a critical piece of Academic Vocabulary Instruction.

Summer Flex Days - 5th Grade

Fifth grade math teachers met on July 15th & 16th.  It was a great two days!  They selected their Professional Learning Teams for the year.  They participated in training on how to facilitate a 4-2-1 free write after Math Congress, in order to deepen student understanding.  They condensed their Problem Solving Unit down to five days, and revised the curriculum guide.  They created a rigorous assessment and located appropriate homework.  They also created an assessment for the Place Value/Powers of Ten Unit and made necessary revisions.  Their division and algebra unit assessments are almost complete, and their division PowerPoint was revised.

Thank you to our wonderful 5th grade math teachers!  It is going to be a great year of learning!

Summer Flex Days - 4th Grade Math

Fourth grade math teachers met July 9th & 10th for professional learning and curriculum design.  We identified important considerations for writing problems that promote critical thinking.  We discussed the characteristics of focused mini-lessons.  We also learned about a writing strategy that can be used following math congress to guide student reflection on the big math ideas.

We worked on the Problem Solving and Number Sense units, beginning with redesigning the common assessments to make them more rigorous.  This was followed by assessing the effectiveness of component parts of the unit, and redesigning portions to increase rigor, engagement, and overall effectiveness.

We had two GREAT days of learning and collaboration!

NCTM Regional Conference

Five Paine Intermediate math teachers attended the National Council of Teachers of Mathematics (NCTM) Regional Conference in November 2013.  We plan to bring all PI Math Teachers some of the great things we learning in future professional development.  Until then, we will bring you our top three takeaways from the conference.

Nancy

1. Using the number line more effectively.

2. Understanding the development of conceptual foundation for teaching fractions.

3. Using reinforcement strategies for basic facts fluency.

Laura

1. Number lines are the central representational tool in teaching numbers.

2. Teaching strategies for mental math and reinforcing with lots of practice and games (exposure) will help students become proficient with numbers.

3. Kim Sutton taught us to be enthusiastic with teaching and use music and dance to help kids understand vocabulary which are the “tools” they will need in their “toolbox”. 

Jana

1. Students should invent their own strategies which will allow them to progress toward more efficient strategies. Students who invent their own strategies progress much more efficiently to number sense/place value. From intuitive numbers to one-to-one correspondence, as long as they are able to invent ways on their own that make sense to them, they will progress to more efficient addition & subtraction. Why should we not teach the algorithm directly? Someone had clearly shown a little girl from a video the algorithm & base ten blocks. When someone forces an algorithm on a child, they lose confidence in their own thinking. The algorithm becomes precedent. This is why the Common Core uses the phrase “develop, discuss and use.”  Algorithms are beautiful inventions if used correctly. (Note: Algorithms were invented by someone at some point in time. It is actually the result of centuries of study by mathematicians).

2. We should not be limited by the Common Core. The mathematicians who influenced the common core said negative numbers don't need to be in there until middle school, but students think in terms of negative numbers. Let them!  Here is how a student solved 61-43:  1-3= (-2).  I took 40 away from 60 and that is 20 then I had to take away 2. So I had to take away 2 from 20 which is 18! <-- This was amazing!!!

3. Precision, reasoning and thinking is at the core of mathematics. Kids would be better off not to come to school than to do ridiculous worksheets about geometry. Must move beyond basic shape recognition. Less is more- focus on the building blocks. Go in depth rather than exposure.

Karen

1. It was so great to see that we are already doing such great things here at PI, especially when the NCTM president spoke about the way to teach math – pose a problem/task, allow students to investigate, then allow the children to discuss their work.  This is what we do every day!

2. I loved the session on fractions, especially all of the free manipulatives!  I hope to use the number line to help build conceptual understanding when we start working with fractions this year.

3. The pre-algebra session was also great!  I can’t wait to start using some of the problems in my classroom.  They were so engaging, and I can see our students becoming much better problem solvers!

Lisa

1. We were in one session with the NCTM President called “It’s Raining Rich Problems!”  She said to never “pull the pencil out of the child’s hand by showing them”.  Rather, question them to further their thinking.   She said productive struggle is a good thing; that is how kids really learn.

2.  She mentioned the 5 practices for orchestrating mathematical discussions:  1) Anticipate (work the problems yourself and have an idea of the strategies that may be used by children), 2) Monitor (while students are working, converse with them and decide which questions will further their thinking), 3) Select (select strategies that will be presented for class discussion), 4) Sequencing (decide which order these strategies should be discussed to scaffold learning), and 5) Connecting (help kids connect the ideas).  All of this sounds just like our constructing tasks and congress.

3.  Regarding constructing conceptual knowledge first, one instructor stated, “Once you teach a procedure first, it is nearly impossible for students to go back and understand the reasons why behind it”; they block that out once the quick procedure is revealed.

Sorry that it took me so long to post this information.  We will be incorporating what we learned into CAD discussions and future PD sessions.

Writing Rigorous Assessment Questions

In our professional learning session today, our math teachers analyzed a sample of rigorous assessment questions. We developed a list of the characteristics we saw in these questions:

• Cover multiple standards in one question
• Connect multiple concepts
• Connect multiple skills
• Most answers are not obvious
• Require deeper, logical, critical thinking
• Some are open-ended; must explain “why”
• Require understanding and use of math vocabulary
• Multi-step/hidden questions
• Multiple choice answers include common misconceptions/distractors
• There are not any explicit clues in the problems
• Can use multiple strategies; several required working backwards
• Some focus on what something is “NOT”
• Some are wordy; can cause loss of focus
• The yes/no examples are “ramped up”
• Goes beyond level of recall/identification; student must analyze/construct/apply
• Must have stamina to complete

We started the process of writing questions that contain these characteristics.  We will consider these factors when writing menu problems, independent performance tasks, and assessments.  Since students spend a significant amount of time working collaboratively, it was suggested that we consider providing students with an independent performance task, after each segment (congress) of an investigation.  This will allow them an opportunity to apply what they have learned, and also become independent thinkers.

We will continue to work on developing these questions.  Thank you for your hard work!  

We have the best math teachers!!!