Category Archives: Connecting Ideas

Assessment, Connecting Ideas, Questions

Multiplication Fact Fluency prototype – feedback requested

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I am concerned that we are conflating automaticity with fluency.  How might we get clear on the difference?

From Assessing Basic Fact Fluency by Gina Kling and Jennifer M. Bay-Williams:

Think about how you assess reading fluency. Does your assessment plan involve listening and observing as children read as well as asking reading comprehension questions? Now imagine what you might learn about students’ reading fluency if you used only timed quizzes. How would your confidence in your assessment change?

When I use Google to search for sample “multiplication fluency assessments, worksheets from TPT show up.If you haven’t yet, it is important to stop and read three articles:

From Fluency: Simply Fast and Accurate? I Think Not! by Linda Gojak:

Building fluency should involve more than speed and accuracy. It must reach beyond procedures and computation.

From Fluency without Fear by Jo Boaler:

The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense.

Ok, so how do we assess fluency? Do we have common language for mathematical fluency?

From  Principles to Actions: Ensuring Mathematical Success for All: 

Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Let’s focus this 3rd grade standard:

Multiply and divide within 100.

CCSS.MATH.CONTENT.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

 

Do any of the fluency assessments from the above Google search help us assess fluency?

What if we try a different type of assessment? An assessment that involves listening and observing as children compute, reason, and respond.

What if we confer with learners individually, just like we do with reading assessments, to listen, record, and encourage learners as they think, reason, and compute?

I need, want, and invite your feedback on the following prototype.  I hope that I have constructed a viable argument and I seek your constructive critique.

Multiplication Fluency (within 100)
Conferring with Mathematicians

Section 1 asks students if they know their multiplication facts. We intentionally ask these questions because of John Hattie’s work on student expectations of self – effect size of 1.44.

Section 2 checks for accuracy and efficiency.  The teacher will code the student’s response as recall, uses a strategy, or skip counts.  The first 8 facts are common for all students. The next 8 facts can be customized for each student based on their responses to easiest and hardest.

 Section 3 checks for accuracy and flexibility.  In the previous section, the teacher gave the multiplication expression and the student responded with the product.  Now it is reversed. The teacher gives the answer and student states an expression and are asked if they know another way.

Section 3 also checks for accuracy and flexibility using images from #UnitChat.  Students are asked how many they see and how do they see them.  If they skip count, their answer is confirmed, and they are asked if they can say or write it again using multiplication.

If you open this Multiplication Fluency (within 100) pdf, you will find each image on its own page so students can touch to count when needed.

Will you take time to offer actionable, growth-oriented feedback using I like…, I wonder…, and What if… to help clarify or improve the assessment?

Thank you in advance.

Connecting Ideas, Learning, Professional Development Plans, Reading

Summer Learning 2019 – Choices and VTR

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How do we learn and grow when we are apart? We workshop, plan, play, rest, and read to name just a few of our actions and strategies.

We make a commitment to read and learn every summer.

Below is the 2019 Summer Learning flyer announcing the choices for this summer.

In case you are interested, links to reviews of each book are shared below as well as the set of TED Talks for Voices from Diversity. #SoGood

Big Potential and The Power of Moments are repeats from last summer’s list because of faculty/staff engagement and enthusiasm. Blindspot and Developing Assessment-Capable Visible Learners are being used in book study groups during the current school year.  We hope to harness the power of the re-read and spread this ideas.

We will continue to use the Visible Thinking Routine Sentence-Phrase-Word to notice and note important, thought-provoking ideas. This routine aims to illuminate what the reader finds important and worthwhile.

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

However, the power and promise of this routine lies in the discussion of why a particular word, a single phrase, and a sentence stood out for each individual in the group as the catalyst for rich discussion . It is in these discussions that learners must justify their choices and explain what it was that spoke to them in each of their choices. (Ritchhart, 208 pag.)

What are you reading/watching/doing to grow as a learner over the summer? Please feel invited and encouraged to watch us (or join us) learn by following #TrinityLearns and #TrinityReads in June and July.

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

#LL2LU, Assessment, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions

#TrinityLearns Leading Learners to Level Up as a TEAM (#LL2LU) Part 2

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Continuing our work from last month, Trinity School’s Assessment Committee continues to grapple with the following questions.

As a team, how are we united (aligned) in our understanding and assessment of learning?  How might we grow our assessment literacy, understanding, and actions to focus on learning, assign competence, and empower learners to become agents of learning?

Under the leadership of Thomas Benefield (@yerlifeguard) and Becky Holden (@BHolden86), Trinity School’s Assessment Committee we continue our commitment to read and take action on Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill by Nancy Frey, John Hattie, Douglas Fisher.  

Below is our agenda for the April meeting where we have begun to grapple with growing our understanding together.

As a team of teachers representing all grade-levels at our school, we chose to analyze student work together and hold a norming meeting to explore and learn one way to help our grade-level teams calibrate and clarify expectations around collaboration and citizenship.

To ensure that all voices were heard, we started with quiet reading time to preview the draft of the learning progressions.  As we did last month,  we used a Google form (shown below) to record everyone’s initial thinking around the level of work based on the drafted learning progressions for Working Cooperatively and Displays Respect.

The artifact, in this case, was a two minute video that offers a glimpse of partner work. (The video is not shared in this post, but a screen shot of one second is shown below.)

Using the Google form continues to be critically important. Everyone’s initial thinking was made visible to the team. Look at the results from our initial thinking.

As you can see, we were all over the place in our interpretation of the meaning and expectations described in our learning progressions.

As a team of assessment leaders, we had anticipated this result. You can see how this might be problematic for students in different sections with different teachers, right?

High-functioning teams that focus on learning must calibrate their understanding of what is essential to learn so that all students are assessed fairly and equitably.

What happened next was nothing short of magical.

First, we discussed our leveling with one partner to explain our reasoning and understanding. It was quiet, calm, and intense.  As partners listened to each other, different interpretations and points of view were represented.  When enough time passed, we returned to the whole group setting and discussed. Again, magical! Everyone confidently shared their initial level assessment and then spoke of how their understanding was shifted by discussing it with someone else.

Then, we took time for individual reflection and leveled the same artifact again, based on our developing common assessment. Just look at the results.

Closer, so much closer to common understanding.

To hone our skills and understanding, we used the same two learning progressions for Works Cooperatively and Displays Respect using video from a different grade level. (The video is not shared in this post, but a screen shot of one second is shown below.)

Again, more closely aligned understanding.

What can be gained when all ideas are made visible to the entire team? How might we learn and grow together by sharing our thinking, seeking feedback, and calibrating with our team?

How do your school’s teams calibrate expectations, shared values, and common understanding?

What actions will we take to become stronger and clearer as a team?

Frey, Nancy, et al. Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill. Corwin Literacy, 2018.

#LL2LU, Assessment, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions

#TrinityLearns Leading Learners to Level Up as a TEAM (#LL2LU)

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As a team, how are we united (aligned) in our understanding and assessment of learning?  How might we grow our assessment literacy, understanding, and actions to focus on learning, assign competence, and empower learners to become agents of learning?

Under the leadership of Thomas Benefield (@yerlifeguard) and Becky Holden (@BHolden86), Trinity School’s Assessment Committee made a commitment to read and take action on Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill by Nancy Frey, John Hattie, Douglas Fisher.  The committee has met approximately once a month to study, discuss, and learn more about growing our young learners as capable, independent, self-correcting, and self-reliant learners.  

Below is our agenda for the March meeting where we have begun to grapple with growing our understanding together.

As a team of teachers representing all grade-levels at our school, we chose to analyze student work together and hold a norming meeting to explore and learn one way to help our grade-level teams calibrate and clarify expectations.

To ensure that all voices were heard, we started with quiet reading time and used a Google form (shown below) to record everyone’s initial thinking around the level of work based on the given learning progressions for Making Thinking Visible and Using Text Evidence.  

Screen Shot 2019-04-10 at 7.18.23 PM

Using the Google form was critically important. Everyone’s initial thinking was made visible to the team. Look at the results from our initial thinking.

As you can see, we were all over the place in our interpretation of the meaning and expectations described in our learning progressions.  It was eye-opening.

As a team of assessment leaders, we had anticipated this result. You can see how this might be problematic for students in different sections with different teachers, right?

High-functioning teams that focus on learning must calibrate their understanding of what is essential to learn so that all students are assessed fairly and equitably.

What happened next was nothing short of magical.

First, we discussed our leveling with one partner to explain our reasoning and understanding. It was quiet, calm, and intense.  As partners listened to each other, different interpretations and points of view were represented.  When enough time passed, we returned to the whole group setting and discussed. Again, magical! Everyone confidently shared their initial level assessment and then spoke of how their understanding was shifted by discussing it with someone else.

What can be gained when all ideas are made visible to the entire team? How might we learn and grow together by sharing our thinking, seeking feedback, and calibrating with our team?

How do your school’s teams calibrate expectations, shared values, and common understanding?

Frey, Nancy, et al. Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill. Corwin Literacy, 2018.

Connecting Ideas, Creativity, Professional Development Plans

Book study: #ChoralCounting and #CountingCollections – session 2 #TrinityLearns

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As a community, we are focused on high-quality instruction that leads to deep understanding.  The teachers of our youngest learners take action to develop young, strong mathematicians.  Together, we are studying Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom to deepen and strengthen our understanding of learning and teaching early numeracy.

Counting is a vibrant part of early learning about mathematics. Young children are constantly counting as they make sense of their world. [Franke, Kindle Locations 490-491}

For our second session together, we turned our attention to choral counting and what we learn when we listen to the diverse thinking of the learners in the room.  As you can see from the tweets below, our teachers are working with our young students to confirm a sense of belonging while strengthening our culture of being seen, known, and heard by teachers and peers.

Choral Counting gets to the heart of what we want for our mathematical communities. This activity creates space for all students to notice, to wonder, and to pursue interesting ideas. Students and teachers alike wonder together about patterns, and why and how numbers change or stay the same. [Franke, Kindle Locations1526-1528}

In addition to deeper work with choral counting, we continue to empower young learners to count, record, and think.

Learning about counting and cardinality are big ideas in the early grades. Having a collection of items invites children to count to find the total number of objects. As children count, they come to understand the relationship between numbers and quantities and connect counting to cardinality. [Franke, Kindle Locations 501-503}

How do we strengthen and deepen understanding, confidence, and efficacy? Who do we help when learners persevere, show their work, and . . . ? What are ways to empower learners to become self-correcting, self-reliant, and independent?

#TrinityLearns

Franke, Megan L. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom.. Stenhouse. Kindle Edition.

Connecting Ideas, Learning, Professional Development Plans, Questions, Reading

Book study: #ChoralCounting and #CountingCollections – session 1 #TrinityLearns

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In Making a Case for ‘Timely, Purposeful, Progressive’ PD, Brian Curtin writes

Want to maximize professional-development opportunities? Provide specific content that suits teachers’ most pressing needs—when they need it most. In order to ensure relevancy, teachers must be able to use the new insights they’ve gained right away.

As a community, we are focused on high-quality instruction that leads to deep understanding.  The teachers of our youngest learners take action to develop young, strong mathematicians.  Together, we are studying Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom to deepen and strengthen our understanding of learning and teaching early numeracy.

Prior to our first meeting on February 4, 2019, 16 teachers and administrators committed to learning together by studying the first chapter of Choral Counting and Counting Collections.  The plan for the Feb. 4 meeting is shown at the end of this post and included time to discuss what we read as well as practice together.

We started with this collection.

And ended up with this:

How might we anticipate ways students will show their thinking and record their work?

Were teachers able to use the new insights they’ve gained right away?

The authors of Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom tell us:

These activities help us enact our commitments to equity. We know that a sense of belonging and investment, of being seen, known, and heard by teachers and classmates, is fundamental to creating schools where children and families feel welcome and where they flourish. Because these activities foreground student sense making and cultivate a joy for doing mathematics, they can be powerful tools for teachers to counter narrow views that only a few can identify with mathematics or that mathematics is disconnected from students’ home lives, their communities, and their own interests.

We are motivated and driven to learn more so that we continue to serve our young learners in the spirit of our mission and vision:

Trinity School creates a community of learners in a diverse and distinctly elementary-only environment, in which each child develops the knowledge, skills, and character to achieve his or her unique potential as a responsible, productive, and compassionate member of the School and greater community.

Celebrating the present and preparing our students for the future within a nurturing and caring educational environment, we:

  • Cherish Childhood
  • Deepen Students’ Educational Experience
  • Empower Students in Their Learning

So that our students:

  • Build Academic Foundation
  • Develop Character Foundation
  • Exhibit Continued Curiosity, Creativity, and Confidence

Curtin, Brian. “Making a Case for ‘Timely, Purposeful, Progressive’ PD.” Education Week Teacher, Education Week, 19 Feb. 2019, www.edweek.org/tm/articles/2017/12/06/making-a-case-for-timely-purposeful-progressive.html.

Franke, Meghan L., et al. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Stenhouse Publishers, 2018.

#LL2LU, Connecting Ideas, Creativity, Learning Progressions, Professional Development Plans

Agenda: Embolden Your Inner Mathematician (11.07.18) Week 8

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Week Eight of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can use and connect mathematical representations. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

From Principles to Actions: Ensuring Mathematical Success for All: 

Use and connect mathematical representations.  Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them.

Tasks:

What the research says:

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5

Too often students see mathematics as isolated facts and rules to be memorized. … students are expected to develop deep and connected knowledge of mathematics and are engaged in learning environments rich in use of multiple representations.

Mathematics learning is not a one size fits all approach …, meaning not every child is expected to engage in the mathematics in the same way at the same time. … the diversity of their sense-making approaches is reflected in the diversity of their representations. [p. 140]

Slide deck:

[Cross posted at Sum it up and  Multiply it out]

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.