Enhancing Growth Mindset in Math – Learning together

We asked:

How might we, as a community of learners, grow in our knowledge and understanding to enhance the growth mindset of each of our young learners?

As a team, we have completed Jo Boaler’s How to Learn Math: For Students and have shared our thinking, understanding, and learning.

Blending online and face-to-face learning, we worked through the Stanford units outside of school so that we could explore and learn more when together.

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Here are some of the reflections shared by our team.

As a teacher my goal is to help children approach math and all subject areas with a growth mindset. It is of utmost importance that my students truly know that I believe in them and their ability to succeed!

Everyone my age should know that you should never equate being good at math with speed. Just because someone is a slower problem solver does not mean that they are a weak math student. Rather, sometimes the slower math thinkers are the strongest math thinkers because they are thinking about the problem on a deeper level. Being good at math is about being able to think deeply about the problem and making connections with it.

When talking to yourself about your work and learning new things, reminding yourself that you can try harder and improve is critical to potential success.  People are more willing to persevere through difficult tasks (and moments in life) when they engage in positive self talk.  

Mistakes and struggling, in life and in math, are the keys to learning, brain growth, and success.

Thinking slowly and deeply about math and new ideas is good and advantageous to your learning and growth.

Taking the time to think deeply about math problems is much more important than solving problems quickly.  The best mathematicians are the ones who embrace challenges and maintain a determined attitude when they do not arrive at quick and easy solutions.  

Number flexibility is so powerful for [students]. I love discussing how different students can arrive at the same answer but with multiple strategies. 

Working with others, hearing different strategies, and working strategically through problems with a group helps to look at problems in many different ways.

“I am giving you this feedback because I believe in you.”  As teachers, we always try to convey implicitly that we believe in our students, and that they are valued and loved in our class.  However, that explicit message is extraordinary.  It changes the entire perception of corrections or modifications to an essay–from “This is wrong, you need to make it right” to “I want to help you make this the best it can be,” a message we always intended to convey, but may not have been perceived.  

Good math thinkers think deeply and ask questions rather than speeding through for an answer.

Math is a topic that is filled with connections between big ideas.  Numbers are meant to be manipulated, and answers can be obtained through numerous pathways.  People who practice reasoning, discuss ideas with others, have a growth-mindset, and use positive mathematical strategies (as opposed to memorization) are the most successful.

We learn and share.

#ILoveMySchool

VTR: Sentence-Phrase-Word to dig deeper into Standards for Mathematical Practice

From Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners:

Sentence-Phrase-Word helps leaners to engage with and make meaning from text with a particular focus on capturing the essence of the test or “what speaks to you.” It fosters enhanced discussion while drawing attention to the power of language. (Ritchhart, Church, Morrison, 207 pag.)

Screen Shot 2014-10-19 at 7.26.45 PMWhat if we read and learn together, as a team? How might we develop deeper understanding?

Screen Shot 2014-10-19 at 7.29.46 PMAs a team of learners, we first read Make sense of problems and persevere in solving them independently and highlighted a sentence, phrase, and work that resonated with us.  In round robin fashion, we read aloud our selected sentence so that every member of the team heard what every other member of the team felt was important.  Just the act of hearing another voice read and callout an idea was impactful.

After completing the Sentence-Phrase-Word Visible Thinking Routine for Make sense of problems and persevere in solving them, we asked everyone to take another Standard for Mathematical Practice to read and markup, highlighting a sentence, a phrase, and a word.

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We divided into teams where each of the remaining Standards of Mathematical Practice were represented.  Each learner shared the SMP that they read highlighting a selected sentence, phrase, and word. My notes are shared below. I was amazed at the new ideas I heard from my colleagues when using this routine.

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Seek diversity of thought. Listen to others.  Hear differently. Promote engagement, understanding, and independence for all.

Learn.


Ritchhart, Ron, Mark Church, and Karin Morrison. “Sentence-Phrase-Word.”Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. 207-11. Print.

 

Lesson and Assessment Design – #T3Learns

What are we intentional about in our planning, process, and implementation?

  • Are the learning targets clear and explicit?
  • What are important check points and questions to guide the community to know if learning is occurring?
  • Is there a plan for actions needed when we learn we must pivot?

On Saturday, a small cadre of T3 Instructors gathered to learn together, to explore learning progressions, and to dive deeper in understanding of the Standards for Mathematical Practice.

The pitch:

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Jennifer and I fleshed out the essential learning in more detail:

  • I can design lessons anchored in CCSS or NGSS.
    • I can design a lesson incorporating national standards, an interactive TI-Nspire document, a learning progression, and a formative assessment plan.
    • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can design a learning progression for a skill, competency, or process.
    • I can use student-friendly language when writing “I can…” statements.
    • I can design a leveled assessment for students based on a learning progression.
  • I can collaborate with colleagues to design and refine lessons and assessments.
    • I can calibrate learning progressions with CCSS and/or NGSS.
    • I can calibrate learning progressions with colleagues by giving and receiving growth mindset oriented feedback, i.e. I can offer actionable feedback to colleagues using I like… I wonder… what if…
    • I can refine my learning progressions and assessments using feedback from colleagues.

The first morning session offered our friends and colleagues an opportunity to experience a low-floor-high-ceiling task from Jo Boaler combined with a SMP learning progression.  After the break, we transitioned to explore the Standards for Mathematical Practice in community. The afternoon session’s challenge was to redesign a lesson to incorporate the design components experienced in the morning session.

Don’t miss the tweets from this session.

Here are snippets of the feedback:

I came expecting…

  • To learn about good pedagogy and experience in real time examples of the same. To improve my own skills with lesson design and good pedagogy.
  • Actually, I came expecting a great workshop. I was not disappointed. I came expecting that there would be more focus using the TI-Nspire technology (directly). However, the structure and design was like none other…challenging at first…but then stimulating!
  • to learn how to be more deliberate in creating lessons. Both for the students I mentor and for T3 workshops.
  • I came expecting to deepen my knowledge of lesson design and assessment and to be challenged to incorporate more of this type of teaching into my classes.

I have gotten…

  • so much more than I anticipated. I learned how to begin writing clear “I can” statements. I also have been enriched by those around me. Picking the brains of others has always been a win!
  • More than I bargained. The PD was more of an institute. It seemed to have break-out sessions where I could learn through collaboration, participation, and then challenging direct instruction, … and more!
  • a clear mind map of the process involved in designing lessons. A clarification of what learning progressions are. Modeling skills for when I present trainings. Strengthening my understanding of the 8 math practices.
  • a better idea of a learning progression within a single goal. I think I had not really thought about progressions within a single lesson before. Thanks for opening my eyes to applying it to individual lesson goals.

I still need (or want)…

  • To keep practicing to gain a higher level of expertise and comfort with good lesson design. Seeing how seamlessly these high quality practices can be integrated into lessons inspires me to delve into the resources provided and learn more about them. I appreciate the opportunity to stay connected as I continue to learn.
  • days like this where I can collaborate and get feedback on activities that will improve my teaching and delivery of professional development
  • I want to get better at writing the “I can” statements that are specific to a lesson.
  • I want to keep learning about the use of the five practices and formative assessment.

We want to see more collaborative productive struggle, pathways for success, opportunities for self- and formative assessment, productive conversation to learn, and more.

As Jennifer always says … and so the journey continues…

[Cross-posted at Easing the Hurry Syndrome]

 

Deep Dive into Standards of Mathematical Practice

As a team, we commit to make learning pathways visible. We are working on both horizontal and vertical alignment.  We seek to calibrate our practices with national standards.

On Friday afternoon, we met to take a deep dive into the Standards of Mathematical Practice. Jennifer Wilson joined us to coach, facilitate, and learn. We are grateful for her collaboration, inspiration, and guidance.

The pitch:

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The plan:

Goals:

  • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can begin to design lessons incorporating national standards, a learning progression, and a formative assessment plan.

Norms:

  • Safe space
    • I can talk about what I know, and I can talk about what I don’t know.
    • I can be brave, vulnerable, kind, and considerate to myself and others while learning.
  • Celebrate opportunities to learn
    • I can learn from mistakes, and I can celebrate what I thought before and now know.

Resources:

Learning Plan:

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The learning progressions:

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The slide deck:

As a community of learners, we

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#ILoveMySchool

Math, Mindset, and Learning Progressions – #LL2LU w/@katonims129

One of the hallmarks of learning at Trinity School is Faculty/Staff Forum, our peer-to-peer professional development. Today, Kato Nims and I facilitated as session on math, mindset, and learning progressions.

The pitch:

Title: Math, Mindset, & Learning Progressions

Facilitators: Kato Nims and Jill Gough

Description: Does a learning progression empower and embolden the learn to locate where they are and ask target questions to make progress: Come collaborate with others to tackle a task or two using a learning progression as a self- and formative assessment tool to experience a student’s point of view.

Prerequisites: None. Bring a pencil or colored pen, your growth mindset, and a partner.

The plan:

Our norms:

    • Safe space
      • I can talk about what I know, and I can talk about what I don’t know.
      • I can be brave, vulnerable, kind, and considerate to myself and others while learning.
    • Celebrate opportunities to learn
      • I can learn from mistakes, and I can celebrate what I thought before and now know.

The slide-deck:

Sample feedback and reflections:

This activity helped me see solutions from multiple lenses. Even though the learning progressions were math-based, I can see the potential for using them in science…with some tweaking. When I present STEM challenges to my students I encourage them to use trial and error and to redesign and improve their work. I need to make learning progressions for the next challenge I present!

Connect – I know children need the language to more clearly express their needs in math. They also need to know what they can do instead of saying “I can’t” because they can do something!  Extend – I came away with a better idea of how to quickly assess my students’ levels at the end of a lesson and that allowing time to work with a partner or in a group is very important to extending my students’ learning.  Challenge – to continue to do the work of getting our learning progressions written and finding the time to collaborate as a team.

Connect: Kids need to know what their goals are, as do their teachers. Kids should be able to solve problems in multiple ways. Extend: Kids can have more than one learning progression that they’re working on at once.
Challenge: Allowing the class to explain what progression they are on with me jumping in to help them. :-) Becoming comfortable adding these into the classroom daily. It’s been hard for me going from saying state standards for 10 years going to this, but I think this is actually more beneficial!

While I don’t teach math on a daily basis, I found this session beneficial because I had an opportunity to practice using learning progressions.

It was very valuable to actually experience a student’s perspective while going through a learning progression.

#ILoveMySchool

MyLearningEdu 1.5 (week 5) – Learning Together

How might we learn, reflect, and share?  What if we take a moment of learning and share it with others?

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  1. Read one (or more) of the following blog posts:
  2. Add a Share button to you blog posts to make it easy for others to share your blog posts.
  3. Reflect, write, and post. Read and comment on posts from at least two others in ourMyLearning 1.5 cadre.  You might consider using the following protocol for your comments:
    • I like…
    • I wish…
    • I wonder…
    • I want to know more about…


 

SMP2: Reason Abstractly and Quantitatively #LL2LU (Take 2)

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We want every learner in our care to be able to say

I can reason abstractly and quantitatively.
(CCSS.MATH.PRACTICE.MP2)

But…What if I think I can’t? What if I have no idea how to contextualize and decontextualize a situation? How might we offer a pathway for success?

We have studied this practice for a while, making sense of what it means for students to contextualize and decontextualize when solving a problem.

Students reason abstractly and quantitatively when solving problems with area and volume. Calculus students reason abstractly and quantitatively when solving related rates problems. In what other types of problem do the units help you not only reason about the given quantities but make sense of the computations involved?

What about these problems from The Official SAT Study Guide, The College Board and Educational Testing Service, 2009. How would your students solve them? How would you help students who are struggling with the problems solve them?

There are g gallons of paint available to paint a house. After n gallons have been used, then, in terms of g and n, what percent of the pain has not been used?
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A salesperson’s commission is k percent of the selling price of a car. Which of the following represents the commission, in dollar, on 2 cars that sold for $14,000 each?
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In our previous post, SMP-2 Reason Abstractly and Quantitatively #LL2LU (Take 1), we offered a pathway to I can reason abstractly and quantitatively. What if we offer a second pathway for reasoning abstractly and quantitatively?

Level 4:
I can create multiple coherent representations of a task by detailing solution pathways, and I can show connections between representations.

Level 3:
I can create a coherent representation of the task at hand by detailing a solution pathway that includes a beginning, middle, and end.   

Beginning:
I can identify and connect the units involved using an equation, graph, or table.

Middle:
I can attend to and document the meaning of quantities throughout the problem-solving process.

End:
I can contextualize a solution to make sense of the quantity and the relationship in the task and to offer a conclusion.

Level 2:
I can periodically stop and check to see if numbers, variables, and units make sense while I am working mathematically to solve a task.

Level 1:
I can decontextualize a task to represent it symbolically as an expression, equation, table, or graph, and I can make sense of quantities and their relationships in problem situations.

What evidence of contextualizing and decontextualizing do you see in the work below?

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[Cross-posted on Easing the Hurry Syndrome]

Seeking brightspots and dollups of feedback about learning and growth.

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