Tag Archives: curriculum

Recap: NCTM 2017

San Antonio, CA , April 2017
I have summarized each session with some simple (•) bulleted notes, red underline to encapsulate my major take-aways, and occasionally a brief italicized commentary.


Math Task Makeover with Desmos Activity Builder — Michael Fenton (Desmos), Jed Butler (Heritage HS), Bob Lochel (Hatboro-Horsham High School)

  • The Big Take-Away = Use Desmos activities to generate intellectual need to learn the lesson objective.”
  • Generate need for Graph of a Linear Inequalities ….

  • Generate need for Definition of Ellipses …

  • Start with informal investigation, then move to formal language.
  • Teacher facilitation is key.
  • Where to Learn more: learn.desmos.com

I’ve got to starting using the overlay function!


Numberless Word Problems in the Elementary Grades — Brian Bushart & Regina Payne (Round Rock ISD)

  • The Big Take-Away = Have students make sense of word problems prior to computation by removing the numbers.”
  • The origin: Press kids to stop just circling numbers in word problems and applying random operation.
  • Not all day every day. It is a tool for sense making.
  • Focus on the relationship and the operation, formal language, and what the question would be, not the answer.
  • #numberlesswp

This makes sense for secondary grades as well.


Rich Tasks as Landmarks for Students to Use in Navigating Their Mathematical Learning Journey — Peg Cagle (LAUSD)

  • The Big Take-Away = Students’ work on Landmark Tasks throughout the year that should be visible in the classroom so that students can map their learning.”
  • We don’t take advantage enough of narrative in math class.
  • “Imagine shrinking down an entire map to the size of an index card. All the details get lost and the map becomes unreadable. What are the landmarks that will help students navigate the mathematical landscape”.
  • Peg presented the criteria for a Landmark Task …

  • … and presented us with a LandmarkTask …

Tied Up in Knots: In your groups, measure the length, in centimeters, of the piece of rope that you have. Then tie a single overhand knot and remeasure the length. Repeat the process several times. Create a data table, graph and equation relating the number of knots to the the length of the rope.

  • … then she analyzed the task according to the criteria …

  • … and showed how this landmark was made visible in her classroom.

  • The Speech Bubbles were created by the students to make comments on other groups’ work.
  1. This is the second year in a row at this conference that I have seen Peg give a year-long, big picture vision of using tasks in the classroom.
  2. This is also the third presenter who has mentioned some variation the Speech Bubbles. Time to use them in my classroom.
  3. Peg made a statement that has me thinking deeply and that I have quoted several times already: “Students have ample amounts of robust evidence that they are not good in math.” We need to help them overcome that.

Changing Teacher Practices: Transforming Teaching 101 to PD 101 — Audrey Mendivil (San Diego County)

  • The Big Take-Away = Shift from Professional Development to Professional Learning.”
  • 5 Principles of Effective PD
    1. On-Going
    2. Support during implementation
    3. Model new practices
    4. Variety of approaches and active engagement
    5. Specific to discipline/grade level
  • Shift from Professional Development to Professional Learning

  • How to Change:
    1. Small Steps. Stick to only 2-3 short term goals.
    2. Rethink Our Norms:

  • Why PD often FailsHow can we set-up for success?
    1) Top-Down Decisions: How can you include teachers in the decision making process?
    2) Little or no support in transferring ideas to the classroom: What support is available?
    3) Idea that teachers need to be fixed: How are you communicating your why?
    4) Lack of variety in delivery modes: How can you differentiate for teachers?
  • Essential Elements. Audrey took us through a terrific activity for those who create Professional Learning experiences. She gave a sets of cards that were color coded, and asked us to work together to sort them into 4-6 groups, and then name the groups.
    She then shared how she grouped them (which is what the color scheme was for). The idea was to take ALL the things that we want teachers to know and do and rather than create a checklist for them, cluster these concepts into Themes or Essential Elements and have teachers learn that.

  1. This was yet another session at NCTM that focused on Vision and the need to put the WHY in front of teachers.
  2. The re-structuring of the norms resonated with me. I’m still thinking deeply on this one. The norms drive the culture of the meetings, so they offer great leverage.
  3. In her call to keep the list of goals short, Audrey discussed the need to set short-term, intermediate and long-term goals. This falls in line with the concept of “leading and lagging indicators.” Student data may take awhile to improve (lagging) so what are the improvements in teacher moves that we can credit to our PD (leading)?
  4. The objective of the card sort activity gets at the heart of what I see killing most PD in districts … too many short-lived initiatives. Keep the broader concepts in mind. Bigger, slower moving targets are easier to hit. 

The Struggle is Real: Tasks, Academic Status, and Productive Problem Solving — Geoff Krall (New Tech Network

  • The Big Take-Away = Developing a culture of productive struggle requires holistic vigilance on the relationships between Quality Tasks, Effective Facilitation & Academic Safety.

  • Protocols for Problem Solving
    1) Make it visual
    2) Estimate Before Solving
  • Record what students know…
    vs what they are assessed on.
  • Promoting Access:
    Example: Make the smallest (or largest) difference by filling in numbers 1-9 no more than one time each.

I am challenged by Geoff’s two graphs of the linear regression of student growth. My Claims-Based Grading needs a little more work in the area of reflecting cumulative knowledge rather than recent learning.


Logarithmic Earthquake Project: An Algebra 2 Project with Real Applications — Tanisha Fitzgerald-Williams & Beverly Heigre (Notre Dame High School)

  • The Big Take-Away = Have students view videos of earthquake damage and do their own research on Richter Scale, before formal presentation of calculating Magnitude difference with Logarithms.”
  • Step 1: Research

  • Step 2: Calculations

 

 

 

 

  • Step 3: Student Groups make Presentations
  • Note: Tanisha & Beverly also have students offer possible humane response to victims of earthquake presented.
  • There is a google drive folder available that contains materials for this projects: goo.gl/Y197YR

Clothesline: The Master Number Sense Maker — Chris Shore (Me)

  • The Big Take-Away = Number sense and conceptual understanding of current content can be taught simultaneously with Clothesline Math.”
  • I presented the power of the Clothesline to teach Algebra, Geometry and Statistics.
  • clotheslinemath.com
  • #clotheslinemath

There were at least 5 sessions at NCTM Annual in which the Clothesline was a part or the focus of the presentation. 


Fun Sidenote: The ceiling rafters and the carpet print of the convention center had the same Geometric Pattern. I am sure there is lesson to be created out of this.


There are videos of keynotes, ShadowCon and Ignite
at NCTM’s Conference 2017 web page.


The city of San Antonio enhanced an already fantastic trip!

 

 

 

Re-Cap: NCSM 2016

 

Oakland, CA , April 2016NCSM Logo

I have summarized each session with some simple (•) bulleted notes, red underline quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.


Game-Based Learning: The Hype is Starting to Give Way to Some Surprising Substance  — Keith Devlin (Stanford)

  • Pic Keith_DevlinBig Take-Away = Start with the thinking (which is the more important), then follow with the notation.
  • The “Symbolic Barrier”: Symbols are a terrific way to use mathematics, but a horrible way to learn them.
  • The vast majority of our population is taught symbolic notation, yet most need mathematical thinking.
  • Students using Dragon Box Algebra learn the Algebraic thinking needed for solving equations in 90 minutes. However, this ability did not transfer to paper/symbolic test, therefore, both are needed.
  • We teach students to play music, before we teach them to read it. The same should be true of mathematics.

Personal note: I’ve had Dr. Devlin’s book, Goodbye Descartes, for almost 20 years; after his talk he signed it for me.


Developing Deeper Student Thinking  and Reflection — Patricia Rogers (Gilroy USD)

  • Big Take-Away = Use “structured” student collaboration to enhance student reflection, and thus student thinking.
  • Good collaboration needs to be: Regular, Brief, Prepared, Open-Minded.
  • 3 Teacher Moves (Phil Daro)
    • Student thinking made visible (to other students, not just the teacher)
    • “Everyone Ready” (ALL students individually prepare themselves to share thinking.)
    • “Make an Expert” (of a students who has viable strategy) then have the rest of the class “Turn and Talk” when productive struggle weakens in order to focus on targeted math topic.
  • Classroom Discussions (Chaplin, O-Connor, Anderson)
    • Wait Time
    • Revoice (The teacher rephrases what the student just said.)
    • Restate (Student(s) rephrase what a student just said.) 
    • Add-on (Student(s) extend or challenge another student’s conjecture.)
    • Apply (Students apply their own reasoning to someone else’s reasoning …” just try it on.”)

I’ve seen the two techniques of revoicing & restating demonstrated a great deal lately and have now been challenged to bring these into my class more often.


SFUSD logoThe San Francisco USD Mathematics Teaching Toolkit: Changing the Practice Along with the Content — Glenn Kenyon & Kathy Bradley (SFUSD)

  • Big Take-Away = Established Vision, Beliefs and Goals before building district curriculum

Vision
“All students will make sense of rigorous mathematics in ways that are creative, interactive, and relevant in heterogeneous classrooms.”

Beliefs
1. All students can and should develop a belief that mathematics is sensible, worthwhile, and doable.
2. All students are capable of making sense of mathematics in ways that are creative, interactive, and relevant.
3. All students can and should engage in rigorous mathematics through rich, challenging tasks.
4. Students’ academic success in mathematics must not be predictable on the basis of race, ethnicity, gender, socioeconomic status, language, religion, sexual orientation, cultural affiliation, or special needs.”

3 Goals
1. Help students express, expand and clarify their own thinking. 2. Help students to listen carefully to one another and negotiate meaning.
3. Help students deepen their reasoning.

“The teaching strategies in the SFUSD Math Teaching Toolkit are designed to support an inquiry-based approached to learning mathematics, with an emphasis on classroom discourse. This approach reflects the shifts of pedagogy required to promote the Common Core Standards for Mathematical Practice.”

  • Unit Design Structure to incorporate tasks

SFUSD Unit Design.png

1) Math Talks
(SMP#3. “Math Talks”, instead of Number Talks, so discussion can broaden {e.g. strategies for computing area})

2) Three-Read Protocol
(Model for close reading of complex math text)
First Read (Teacher Read Aloud) = What is the Situation?
Second Read (Choral Read) = What are the Quantities & Units?
Third Read (Individual Read & Think) = What question can be asked?
This only runs 10-12 minutes. Take away the question to create a rich task.

3) Participation (Group) Quiz A technique to give public feedback on group work. Lists ways a student can contribute (“You can help your group if you can…. create a table, draw a diagram, listen to people’s ideas and ask questions, etc) Also publicly list teacher expectations (e.g. How groups … us shared space? ask question? explain thinking? etc)

  • Video Exemplars & PD modules are available on district web site.
  1. SFUSD has a PHENOMENAL math web site chalked full of resources for supporting teachers implement the vision and the curriculum. Check it out!
  2. The description of their Group Quiz speaks to the need to explicitly teach students how to productively collaborate.
  3. This was the first of three sessions that spoke about the importance of vision. It will be the predominant point that I take home with me from this conference.

Beyond Relevance and Real World: Talking with Teachers About Engagement in Mathematics? — Dan MeyerPic Dan M

  • Big Take-Away = ‘Real World’ does not have to be real, just accessible and engaging.
  • 62% of teachers surveyed : Greatest challenge is “unmotivated” students. Interesting that they didn’t say motivating students was the challenge.
  • Question: Why don’t teachers spend more time developing good questions?
    Teacher Response: “Because we don’t have the time.” (True that.)
    Real Issue: “Lack of creativity. Giving the answers does not require creativity.” (True that, also, but ouch!)
  • A stronger option than the typical “engaging images or context” in a textbook: Redefine Real World. A situation is in the process of becoming real to you if you are able to … 

1. Ask a question about it.
2. Guess about it .
3. Argue about it.


High School Coaching Model: Building Bridges Between Coaching and PLC Culture — Kris Cunningham & Jeanette Scott (Phoenix UHSD)

  • Big Take-Away = Roll out PD through PLC teams.
  • New initiatives first unveiled during PLC team meetings.
  • Most powerful change agent was a lesson study. (1st day by 1 teacher, next day by all teachers)
  • Most teachers took 3-4 years to show change; 4 of 5 teachers showed significant change within 5 years.
  • There exists a Common Lesson Plan format for lessons studies and co-planning.
  • Professional Development certificates tied to evaluations. (i.e. Professional Growth affects evaluation outcome.)

The fact that teachers took 3-4 years to show change aligns with Maggie McGatha’s research shared at last year’s NCSM conference


Practicing the Five Practices: Coaching Teachers to Use Student Work in Planning  — Max Ray-Riek (Math Forum)

  • Big Take-Away = Walk teachers through the 5 Practices of Discourse with student work samples.
  • Max shared with us the Teddy Bear’s Banquet pattern problem. He had us determine the Math Goal for the lesson, and then Anticipate the student responses.
  • Max then offered 16 samples of true student responses (Monitor) and then had us Select and Sequence some of the responses for classroom discourse and share why. We were then asked to Connect the responses to the Math Goal.

This is a great training tool that can be brought into any PLC structure.

I also witnessed Max slyly counting on his fingers. This was his way of giving is all wait time on his prompts. 


Smarter Balance – Making Connections: Eliciting to Acting on Evidence —  Judy Hickman (Director of Mathematics, SBAC)

  • Big Take-Away = When the scoring focus is on Reasoning, students can still score full credit with a minor calculation error, if they show understanding.
  • Do NOT put too much emphasis on Interim Assessments. As “snapshots” they will give you good information, but it will be an incomplete assessment.
  • The authors of the exams were shocked that students answered so few questions correctly.

Four Keys to Effective Mathematics Leadership — Mona Toncheff & Bill Barnes  (Activating the Vision )

 

 

 

 

  • Big Take-Away = Vision needs to be created by ALL stakeholders
  • The Four Keys:

1. Establish a Clear Vision for Mathematics Teaching & Learning
2. Support Visionary Professional Learning for Teachers and Teacher Leaders
3. Develop Systems for Activating the Vision
4. Empower the Vision of Family and Community Engagement

This was the second of three sessions that spoke about the importance of vision. This one stressed the need to have all stakeholders (admin, teachers, classified staff, parents and the business community) in on the creation of the vision. Mona & Bill then asked, “If you were ask 10 people on your campus, ‘What is our vision,’ how many answers would you get?”


The Secret to Leading Sustainable Change: Vision, Focus, Feedback, and Action! — Dr. Tim Kanold (Turning Vision into Action )

  • Big Take-Away = Set the Vision, Help people advance the Vision,  Celebrate Evidence that the people are advancing the Vision, and take Action on the feedback towards the Vision. 
  • Sustainable change requires evidence that the change is bigger than their opinions.
  • Is the work you are doing formative? Meaningful feedback must be followed with results in action by the teacher or teacher team.
  • Meaningful Feedback = F.A.S.T. Action: Fair, Accurate, Specific, Timely. Action from your feedback is required.
  • Mary Beth call. Dr. Kanold told a story of when he was Superintendent of Stevenson HSD. He called a secretary at one of the schools, restated that ‘engagement’ was part their district vision, and asked “What does engagement look like in your job.” That’s keeping the vision in front of the people!
  • The Popeye Moment: Change happens when the moment of moral courage vocalizes what Popeye often said, “That’s all I can stands, cuz I can’t stands n’more!

This was the third of three sessions that spoke about the importance of vision. The story of calling the secretary is tattooed on my brain. Dr. Kanold stressed that the vision should be posted visibly during every PLC meeting, and that any unproductive dialogue can be redirected with the simple statement, “How does this conversation advance this vision?”


A Math Coaching Package — Donna Lione, Rebecca Williams & Chris Shore (Me) (Temecula Valley USD )

 

My colleagues and I presented the framework for developing a comprehensive math program. The details of each of the 8 components will be posted as separate posts.

  • Vision
  • Relationships
  • Humility
  • Influence
  • Passion
  • Faith
  • Focus
  • A Plan

Kicking the Textbook Habit

Textbook FreeI have had several inquiries about an article I wrote many years ago titled, Textbook Free: Kicking the Habit. I am not surprised, because, in these days of Common Core roll-outs with few valid materials, teachers are having to create and find their own curricula. While the article is over a dozen years old, it could not be more timely, so I thought I would make it available again. I hope this helps encourage teachers that using textbooks as a resource instead of as scripture in the era of the New Curriculum can be easy and fun.

Textbook Free: Kicking the Habit

Originally printed in The Math Projects Journal in May 2001:

I kicked the habit! I am no longer a textbook junkie. I no longer rely on my daily fix of some publisher’s bloated curriculum. I am free of my addiction without the help of an arm patch, rehabilitation clinic or twelve-step program. I quit cold turkey. Here’s how.

At my school, the students are issued a math book that they leave at home and each teacher is issued a class set. I usually keep one underneath each desk. This year, however, the librarian informed me on the first day of school that we were out of Geometry textbooks. Our student population had grown so large that our library ran short. In fact, for two to three weeks many of my students would not have a book at home either. There was talk of teachers sharing class sets and photocopying pages for students. I decided to try a different strategy. I took this as a professional challenge to see how long I could teach without a textbook. I knew whatever happened would be a growing experience for me as well as my students.

Well, by no fault of the school library, two to three weeks stretched to seven. By that time, I was well into my “textbook free” strategy, so I just kept the ball rolling…for the rest of the year. I used only 12 assignments from the textbook in those 180 days. Here is how that unique experience of being textbook free has changed my teaching, forever.

Firstly, I am now much more focused on standards. Rather than leafing through the textbook, I looked at my state and district standards, and established my curriculum from those. After all, shouldn’t they be determining what we teach? From there, I grouped the topics into units, and then scheduled individual lessons. This process naturally pared down the number of topics that I taught and allowed me to allocate a full week of instruction to each concept, rather than one day to each section of the textbook.

The second big change that has occurred is the structure of my lessons. Everything from my homework to my instruction has radically changed. My typical textbook free lesson was comprised of three to six problems of various difficulty. Oftentimes, I began a lesson with one to three review problems from previously learned material which applied to the current lesson. This is similar to a traditional warm-up with the exceptions that the problems are very relevant to the new lesson, and not simply arbitrary review.

Sometimes, I began with THE big problem from the previous night’s assignment, and solicited student responses. It is not hard to see that my old practice of dedicating 20 minutes of class time to questions on how to complete the previous homework disappeared. The intent of the class slowly evolved from getting the answers correct to understanding the mathematical principles behind the question.

These introductory problems served as a terrific assessment tool, also. Previously, it was difficult to know how well the students were doing when only a handful of them were asking questions from a truck-load of exercises. However, when the whole class was engaged on the same few problems, it was easy to walk the room and evaluate their performance and understanding.

The introductory questions naturally lead to the main problem or small set of problems that would drive the lesson. The students were engaged in an investigation, project or activity relating to the concept. Each day my students came to class to solve problems, rather than take notes — a huge change from all the previous “textbook years.” This process of problem-solving and investigation consumed the full class period. Gone were the days of having the students start homework in class. I taught the entire class period.

The homework assignments were only one to three problems long and were typically extensions of the day’s topic, not just practice exercises. I had learned from the international comparisons that America is one of the few countries that pushes the drill-n-kill regime and yet we are at the bottom of the performance pile. So I tried to limit both the number and size of my assignments, and to make them more challenging and contextual.

By doing that, I firmly settled the argument regarding the quantity and frequency of homework that students need to be successful. For the skeptics that are still reluctant to abandon their practice of assigning 30 homework problems a night, I have some strong evidence. My class averages led the district on the district final. With this in mind, I can at least make a case that this new homework philosophy is not hurting my students in anyway.

Another significant change was my lesson planning. Rather than writing examples of how to complete an algorithm or creating cute acronyms to remember esoteric rules, I actually wrote lesson plans. I started planning each lesson by asking: “What do I want the students to know? What is their common misconception of the topic? How can I best get them to understand the topic? How can I challenge them within the context of the topic?” I would then try to create a story/context/scenario and a small set of problems that would best develop understanding of that topic. It was so much fun. This change in my approach to lesson planning was actually a reflection of my new attitude towards teaching. My job description truly shifted from covering material to uncovering knowledge.

Focused, standards-based curriculum; in-depth, problem-solving instruction; short, conceptually-based homework assignments. This experience was so exhilarating that I am now a junkie all over again. I traded my old addiction to the textbook, for a new one — creative lesson planning. This is one habit, though, that I never intend to kick.