I went on a 3.14 mile run at the end of the day. The first screenshot was after I rotated the map, although it doesn't show the distance. The second screenshot shows the distance (you may notice my slow down at the end of my run because I answered a phone call - oh well).
This is a simple, short post about today, March 14th. For math folks, it's known as Pi Day. There are so many ways to celebrate Pi Day - getting and eating pies, working with Pi in math problems, and doing a Breakout EDU game about Pi (a colleague of mine, Valerie Sabbag, did that today with her fifth graders). How did I celebrate Pi Day?
I went on a 3.14 mile run at the end of the day. The first screenshot was after I rotated the map, although it doesn't show the distance. The second screenshot shows the distance (you may notice my slow down at the end of my run because I answered a phone call - oh well).
"Curriculums come and go. Standards are here to stay."
This was the phrase that prompted my work with grade level teams on examining the CCSS-Math standards. Elementary school teachers in the Palo Alto Unified School District are in the middle of a pilot year to select new math curriculum that scheduled to be implemented during the 2017-2018 school year. PAUSD has been using Everyday Math for eight years with a lot of conflicting opinions of the curriculum between the staff and parents. There are many schools that have used it with fidelity while some schools have moved onto using other math curricula to meet the needs of their students and align with the Common Core State Standards, including EngageNY. No matter what curriculum teachers use, quality pedagogy that focuses on the success of all students, aligned to the Common Core State Standards and the 8 Mathematical Practices is the key.
I share the belief (and fact) of many that there is no perfect curriculum. My view is that any curriculum acts more like a GPS navigator. Throughout the school year, teachers make professional and purposeful decisions to use supplemental materials to meet the needs of their students. As a result, the progression of lessons in any curriculum is paused or altered. These professional and purposeful decisions is the science of teaching and no curriculum can replace the science of teaching. Instead, the curriculum as a GPS navigator to guide the teacher back on a predetermined path when necessary decisions to change the path are made. Like any road trip, the driver (the teacher) can make purposeful decisions to alter the suggested path (of the curriculum guide).
The biggest part of this analogy is the focus on the destination - meeting the grade level standards. An effective curriculum is designed to bring all students to meet CCSS at the end of the school year. Focusing on the destination of CCSS is the key aspect of the standards mapping activity.
Working with grade level teams, I've lead teachers to read and better understand the CCSS Math standards for their grade levels. It's been a powerful exercise, evidenced by teachers commenting that they "didn't know that was the actual language in the standards," that they didn't have to "teach concepts they've taught before" which saves them time to focus more on the concepts that have been problematic for their students, and that they see how to address "standards at each trimester of the school year." The exercise provided teachers the chance to identify which concepts/standards was important to address at each trimester in order to build understanding that leads to practice and mastery by the end of the school year. Of course, each of the above standards cards is meant to be mastered by the end of the school year, AND having an understanding of the progression of concepts throughout the school year helps gain a bigger picture of the professional and purposeful instructional decisions.
Having a deeper understanding of the Common Core State Standards is definitely an important piece of instruction.
- to know the destination of the school year,
- to know what's important to address at each point of the year and how concepts build,
- to be able to teach to those standards no matter which math curriculum is used (or selected in PAUSD),
- to see curriculum maps as guides to meeting CCSS and professional instructional decisions are far more important,
- to be able to see how "concepts build from grade to grade."
It's definitely important to remember that We don't teach curriculum; we teach students. Be mindful of the standards - the end destination, however, remember we teach students.
Learning takes hard work, understanding, perseverance, making mistakes, and learning from mistakes.
I had the pleasure of supporting two second grade teachers at Fairmeadow Elementary School this week with the use of SVMI's Problem of the Month packets to practice the 8 Mathematical Practices. During week 1 of this Problem of the Month packet, I led the students through Level A in a Number Talk format. Students were able to construct viable arguments and share the strategies they used. It was great to see the students in both second grade classes exercise Math Practice #1 - Make Sense of Problems and Persevere in Solving Them throughout their time working on the levels of their packets.
Last week, I continued supporting the teachers with their SVMI Problem of the Month packet with the project of creating posters to share our thinking. Of course, students are used to sharing their solutions. Most math sheets, activities, packets ask students for the answer and to explain their solution. A great benefit to SVMI's Problem of the Month packets is how the problems are written. Many packets and their levels have been carefully written to allow for multiple solutions, causing students to truly justify their thinking - fostering Math Practice numbers 1, 2, and 3. Students showed great perseverance with making sense of problems, deciding how to attack the problems, constructing viable arguments with clear explanations, and checking their work for labels and clarity.
In our activity, I shared the concept of an explanation poster where students share their thinking, explanation, and strategies. This is an area that I've grown as an instructional coach. In previous years, I called them Solution Posters, but realized having a slight name change to explanation poster shifts the focus from the solution to the explanation. This was definitely evident this year as I observed students putting more of their focus on providing clear explanations.
In that session I also introduced the concept of a status poster. The second grade students were quick to understand the purpose of a status poster. "It's to show my progress." "The poster helps people know what I've done so far." In our discussion, we added that showing a status poster allows classmates and other learners to either get ideas from your work or offer ideas for your next steps. It was really great to see students understand the value of the this process - the value of growth mindset and the iterative process.
Below are pictures of the second grade students from Susan Hoff's and Melissa Hinkle's classes creating their explanation and status posters of SVMI's Problem of the Month packet. Scroll down beyond this first set of pictures to see the work from this week.
This week, we concluded our month's work with SVMI's Problem of the Month packet by sharing our explanation and status posters through a gallery walk. After introducing/reminding students of the process of a gallery walk (the process of admiring the work of the artists/mathematician and being a detective to understand the work behind the piece), I shared the process of providing feedback to classmates on sticky notes. For the second graders, we discussed the process of sharing compliments and questions. When discussing compliments, we talked about the importance of being specific with our positive feedback so our classmates know exactly what they did well, instead of just "Great job." We then moved onto the value of asking questions about the work instead of sharing negative criticism. With examples and sentence stems, we talked about the impact and difference between, "You're wrong," or "You didn't do your math correctly," and "Did you double check your calculations," or "I could understand this better if you included labels." It was definitely an important discussion and setup for our gallery walks. Below are pictures of the compliments and questions from the students to each other.
After a full school year used to explore eight different CCSS-aligned math curricula, PAUSD's elementary education department and its teachers leaders have identified the three curricula to pilot next school year - Investigations - TERC, Everyday Math 4, and engageNY / Eureka Math.
It was quite a process for the district to arrive at this point. This exploration year's primary focus was for sites to explore a variety of Common Core State Standards aligned math curricula. This collaborative exploration strengthened teacher understanding and instructional strategies in relation to the CCSS and built a cohesive teacher leadership group that recommended the three curricula that are worthy of a formal pilot during the 2016-2017 school year.
Yesterday's final math lead meeting that resulted in the three pilot curricula was the culmination of two years of work - identifying the math curricula neighboring district's adopted, reading research, connecting with other math professionals at NCTM, and collectively developing our understanding of CCSS and the Math Practice Standards to help inform our process of exploration and decision. Having had this year of exploration that helped us deepen our understanding also had additional benefits, one of which was that some publishers were still in the process of completing their CCSS-aligned curricula. We found that several neighboring districts that had adopted various curricula were unhappy with their "rushed" decision.
It was an incredibly collaborative process to explore the eight curricula (listed in the image below). The timeline of our exploration year is also included below. Now as we move forward with our three selected curricula for pilot, we will definitely assess the following areas of each curricula:
Extending the learning. I had the pleasure of working with Gina del Fucco, a first grade teacher at Briones Elementary School, throughout the year. We've explored the use of Number Talks as a way for students to explain their mathematical thinking, ReEngagement with MARS Tasks for students to analyze another student's responses, and Problem of the Months for ongoing problem solving.
Gina and I partnered together this week to extend concepts she was teaching her students in geometry. In a conversation together, she shared that her students have learned about 2D shapes and started identifying 3D blocks by their names and attributes. That was a wonderful foundation for the work we did next - turning a (common) 2D design into a 3D block.
During the lesson, we identified familiar vocabulary in geometry with the students - square, sides, corners. With cubes the students had in the classroom, Gina and I introduced the terms faces and edges (we purposefully saved vertices for a future exploration). It was great to see the students work flexibly with the task of taking the 2D design of 6 squares with connecting sides and turning it into a 3D cube with square faces and edges. The students had a lot of fun designing their cubes - some were dies and fortune tellers.
Extending the learning. As an instructional coach, I love the opportunities I get to think about how to apply, synthesize, evaluate, and analyze their learning.
Pro Tip: When you have students creating cubes, direct them to put the scraps from the paper inside the cube. This will give the cube some weight and also help keep its shape.
Families in the Fairmeadow Elementary School community enjoyed a wonderful, hands-on evening at Family Game Night on Wednesday, February 24, 2016. It was such an amazing evening with a full house of students, parents, grandparents, ... in Fairmeadow's Multipurpose Room. As a Math & STEAM Coach, I had the pleasure of sharing in that event, capturing the activities with pictures and videos, and celebrating with the entire school community in its exploration of math games.
-There were over 10 stations of various math games they students enjoyed.
- Parents had the opportunity to play with their children.
- Various math games were available, from a variety of cultures and countries.
- And, of course, this was a wonderful experience that continued to foster positive home-school connections around mathematics.
It's always such an amazing process of hearing the mathematical thinking of students during Math Talks - Number Talks and Dot Talks. As a Math & STEAM TOSA, I've had the pleasure of joining many classes throughout PAUSD and listening to the academic discourse from students from Kindergarten to Fifth grade.
On Tuesday, February 16th, I had the pleasure of hearing a second grader from Susan Hoff's class at Fairmeadow Elementary School share his mathematical thinking. I had just introduced a new Problem of the Month packet and got to listen this his strategy of solving 19 x 3. Enjoy the video I captured. You'll notice he effectively shares his mathematical thinking and math strategies. Through the Number Talks, MARS Tasks, and Problem of the Month packets Mrs. Hoff and I have used with her class it's clear they have really been exercising Math Practices 1 & 3.
Elementary school teachers throughout PAUSD had our staff development day today and I had the pleasure of facilitating the sessions focused on the use of Problem of the Month packets in math. My colleague, Mangla Oza, a math TOSA, and I co-presented to the fifth grade teachers throughout the district during the first session and then to the fourth grade teachers during the second session. It was a wonderful time looking at the use of the Problem of the Month packets and how it touches on the 8 mathematical practices. It was wonderful to see and hear all the mathematical thinking, reasoning, and sharing of ideas during the period of problem solving, the gallery walk, and the debrief time.
After each session, teachers gave Mangla and I very positive feedback. Many said they appreciated the time to just work on problems that really tested their problem solving skills. Many others said they could see their students enjoying the challenge and the chance to share their thinking with their classmates. Everyone who spoke to us told us they mostly appreciated that today's staff development day looked at a familiar topic and not something new. Teachers are definitely overwhelmed with all the new initiatives of this school year. Some of them said it was great to look at the Problem of the Month packets again in light of CCSS and the math practices, and that for whatever reason they had forgotten how powerful the packets are.
It was an incredibly fulfilling morning as a presenter and professional developer.
One specific appreciation I received today that really filled my bucket was from a dear friend and colleague, Valerie Sabbag. In our conversation, Valerie said the message she heard at church on Ash Wednesday focused on thinking of the people in our lives that have made an impact on our lives and have made a positive impact on our lives. She said, "I thought of you and how every time you're at Fairmeadow, you are always so supportive and complimentary of what I do. You always take pictures of what I do and tweet them out and highlight the things I do."
What an incredible bucket-filler! Now, as I write this post, I know I need to just hear the appreciation and take it in. I need to accept it. In reflection, I know I should do that. What I did at that time reflects my humble nature. I responded, "Thank you for filling my bucket. I want you to know that my tweets and compliments are all because you have so many amazing things in your classroom. I just get to spotlight the things you already do. Without your awesome stuff, I wouldn't have anything to tweet about."
Appreciations are given with sincerity. I know I can work on myself and my response to them. I know I can accept the appreciations.
I know I will always live with humility, AND I can take that moment to accept the appreciation.
I've had the pleasure of partnering with Diane Darrow, a fifth grade teacher in the Palo Alto Unified School District, throughout this school year so far on math instruction, setting up her math workshop, using Problem of the Month packets for extensions, analyzing formative assessments, and leading the students in number talks. It's been a pleasure getting the opportunity to watch her students learn and grow.
On Tuesday, December 15th, I led the students in a number talk on fractions. Diane and asked me to design a fractions number talk since her students had been working on fractions during their math workshop. I thought of using the easier operation of adding fractions but setting the challenge in the problem with unlike denominators. The denominators I chose could lead to a large common denominator or a smaller one if the students reduced the fractions first.
As our Number Talk progressed, the students shared responses and strategies that Diane and I both anticipated. Many students were able to see the relationship and equivalencies between fractions. Toward the end of the Number Talk, Diane and I were both incredible impressed by the flexible thinking from one of her fifth graders. Instead of trying to find common denominators with 8 and 10, the student thought of a way to make the denominator (8) of the first fraction (6/8) into the value of 10 in order to match the denominator of the second fraction (6/10). As a result he multiplied 8 by 1.25 in order to have common denominators of 10. What was interesting was he also multiplied the numerator by 1.25 to make it an equivalent fraction and got 7.5 as the numerator. That led to a wonderful conversation of whether you can have decimal numbers in a fraction. What do you think?
On Friday, October 30th, I had the pleasure of leading the third graders in Charlotte Fang's class at Juana Briones Elementary School in a Number Talk and the students were highly engaged, shared strong mathematical thinking, and engaged in powerful academic discourse. This was my second time leading a Number Talk with Mrs. Fang's students and it was great to hear the student name the strategies we discussed during our first Number Talk, such as decomposing, using place values, and using friendly or landmark numbers.
This this Number Talk, I led the students in two related problems, to check their application of strategies and concepts from the first problem to the second. It was great to hear the students' strategies, mathematical thinking, and the academic discourse we had around the two problems in the first image above. As in all Number Talks, I chose the problems 4 + 6 + 5 and 24 + 16 + 25 purposefully to see if the students would be able to make an connections between the two problems. It was great to see some common strategies used across the two problems.
It was truly amazing to see the students work so hard on the math problems, especially when the day was filled with Halloween-themed activities. What an amazing pleasure it was for me to share that Number Talk with them
Open-Ended Problem Stem
My day at Juana Briones Elementary School continued in April McCandless' second grade class. Mrs. McCandless had asked me to demonstrate how to do an Open-Ended Problem Stem with her students from having that activity introduced to her and other math lead teachers in PAUSD earlier the previous week. I had a fun time coming up with the problem so I could demonstrate the format of an Open-Ended Problem Stem while making it engaging with a Halloween-theme.
After beginning with a quick warm-up problem and reviewing the importance of showing our work, including every step so our thinking is clear, and labeling our work, I introduced the problem above. I got scared at a Halloween Party and hid under the table. Eventually I built up my courage and peeked from where I was and saw 19 legs. Who could be at the party?
The students immediately had this confused look on their faces. "How could there be an odd number of legs?" "What?!?!" "Do you get it?" "I don't understand." Those responses were just the reactions I anticipated. After a bit of encouragement to attempt the problem, suggestions to talk with their partners, and to think creatively, the students really into the problem.
It was really great to hear and see the students' increased flexible thinking with the problem. As you can see in the pictures in the above gallery, some ideas included an alien costume with three legs, a pirate's costume with a peg leg, and a costume of an elderly person whose cane was mistaken for a leg.
In my closing, I complimented the students with the lifeskills they showed during the lesson. I twas great to see the students demonstrate perseverance, collaboration with partners and as a table group on a difficult problem, effort, and a growth mindset. Those second graders definitely showed an incredible sense of accomplishment and pride when they reflected on their work.
For me, it was an incredible day being at Juana Briones Elementary School - participating in the Halloween Parade, sharing a Number Talk with Charlotte Fang's third graders, and demonstrating an Open-Ended Problem Stem to April McCandless' second grade students.
How many dots do you see?
Today, Laura Reeves and I were invited to join the Pre-K, transitional Kindergarten, and special education teachers at Greendell for their staff development day. It was a great experience for me since I've seen many of those teachers in previous workshops and trainings.
The first thing about today was learning where Greendell is. Up until today I had no reason to go onto the Greendell campus since workshops with those teachers were often at the district office and the former portable C. I had driven by the sign indicating Greendell's campus for years but I never knew where it was. What a lovely campus it was! Such a gem in the Palo Alto Unified School District.
Dawn, Greendell's principal invited Laura and I to lead a discussion and training on Number Talks/Dot Talks. It was great to examine the structure of Number Talks, discuss how they connect to the Common Core State Standards, and explore the benefits of Number Talks for students and teachers.
One of the best parts of the workshop was the experience for Greendell's teachers to put the practices into place. It was good to see the teachers practice giving their Dot Talks and also play the role of students explaining their mathematical thinking.
I hope to have the opportunity to partner with the Greendell teachers again really soon.
Today was PAUSD's first elementary TOSA Team Meeting of the 2015-2016 school year. It was a wonderful opportunity for all seven of us to sit with Barbara, the Chief Academic Officer for Elementary Education, and the coordinator of the BTSA coaches to discuss our roles as TOSAs / coaches, work out some logistics of leadership teams at school sites, and gather in shared learning and shared objectives.
I had the pleasure and privilege of leading a Number Talk / Math Talk with the TOSA team. I've had many experiences leading Number Talks with my students in first, second, and fifth grades. I've also led training workshops for teachers on how to plan, lead, and reflect on Number Talks. This time I led the Number Talk as if I was speaking to my students, cutting in and out of that when addressing the metacognitive reasons for parts of my Number Talk. Through the Number Talk, my colleagues effectively shared their mathematical thinking and the strategies for how they solved an addition problem with three 3-digit addends. A few members of the TOSA team noticed that I explicitly write down and label the strategies for each method (decomposing, near doubles, partial-sums, ...) and we engaged in a discussion about how that practice helps our students. By identifying the strategy and labeling it on the board next to the method(s), students receive continued exposure to academic language, deepen their understanding of the strategies, and increase the chance they will internalize the mathematical concepts and apply them in new situations and problems.
My closure for the Number Talk was asking my colleagues to share something they learned or re-learned. Barbara's comment highlights the value of Number Talks. Barbara, like any adult who experiences Number Talks for the first time(s) may have a few ways to solve a given problem, but through the process, they learn many more strategies and also the academic language for those strategies. "My new learning was decomposing."
PAUSD educators throughout the summer had the pleasure and privilege of hearing from Patricia Swanson, Associate Professor of Education at San Jose State University, speak about mathematical practices that addresses the Common Core State Standards. This week, Patty Swanson offered a three day workshop for educators who support fourth and fifth grade students. It was great attend this workshop with academic specialists, teachers across the district, a teacher from the Lucille Packard Children's Hospital, and members of the group DreamCathers.
In this workshop we explored mathematical practices and activities that support children's process of making sense of math. Math is not about memorizing facts and algorithms but making sense of them - constructing meaning.
I was really impressed with the discussions throughout the institute and workshop that focused on equity for all learners. Patty offered ideas and structures that help manage group roles, ensure every member contributes, and holds each group member accountable for the wellness of the entire group.
Some highlights from the institute include:
-The Broken Squares activity that really calls for cooperative group work.
-Explorations of multiplication models and the distributive property with an activity called "Cover Up."
-Discussions that go beyond classroom management into how those systems and structures benefit ALL students and ensure for equity of roles and responsibilities. Clear, purposeful structures like that are essential for all learners.
-Powerful discourse between professionals examining the deeper levels of thinking involved with the eight mathematical practices of the Common Core State Standards
It's been an amazing week being around so many professionals and highly motivated educators this week at the Silicon Valley Mathematics Initiative's Coaching Institute. This was SVMI's 16th annual coaching institute and my fifth year participating in this fabulous professional development event.
In previous years I attended breakout sessions that focused on Lesson Study. Palo Alto Unified School District had quite a large group of teachers attend the institute that worked collaboratively on Lesson Study and Number Talks. I really enjoyed those summers and the impact the things I learned had on me, my teaching, and, ultimately, my students.
This summer I had an equally inspiring experience. This summer, as I began my new role as a match coach/TOSA, I attended the "Content Coaching" breakout group. It was great to be with other math coaches all around the Bay Area to explore the intricacies and nuances of coaching structures, communication styles, and mindsets.
Some highlights from this year's institute include:
-The activities with the Problem of the Month(s) were, as always, powerful, enlightening, and challenging. Participants of the institute got to work on the new POMs of 2015 titled, "Get to the Point" and "Ride Around." I heard similar comments from people who were familiar with POM and those who were new to those types of problems and the format suggested for POM. "Each level provides challenge for all students at all levels." "I really appreciate the gallery walk experience." "The chance to make a status poster was really freeing. It helped give us a chance to show what we know right now and not worry about having the problem solved with an explanation yet."
-Language matters. In our whole-group gatherings, we explored the importance of language for all students. Are we using language in our speech, directions, and/or word problems that are accessible for ALL students? Are we mindful of the intricacies and nuances of our language and idioms that often leads to misunderstandings and misconceptions in our students?
-Mindsets. No matter how much anyone has explored mindsets it's always powerful to examine mindsets again (even if you're Carol Dweck because she's most likely continuing her research on mindset). In the whole-group gatherings, we discussed language and The Power of Yet. This is a link to Carol Dweck's TEDx Talk in November 2014. The following is the embedded video from YouTube.
-Models. We examined the use and power of models to improve decisions. Modeling links mathematics and statistics to everyday life, work, and decision-making.
-Five Productive Talk Moves:
Asking students to restate someone else's thinking
Do you agree or disagree and why?
Would someone like to add on?
Using wait time.
-Language coaches can use that encourages reflection.
-Analysis of the roles of a coach as a collaborator, a mentor, and a leader.
If you have never attended a SVMI Coaching Institute, I highly recommend it. It is a very powerful professional development opportunity.
Math & STEAM Coach / TOSA in Palo Alto Unified School District.