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Oops! I made a mistake (Oops! I did it again)

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Oops! I made a mistake (Oops! I did it again)

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Mark has the moves.

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Using sticky notes to play with possibilities!

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Rehumanizing Math Through Collecting and Representing Data - Amy Vickers

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Rehumanizing Math Through Collecting and Representing Data - Amy Vickers

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Handout for the Open Middle activity we worked on together.

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John Lewis - Get in the Way - The Nashville Sit-Ins (PBS) 

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John Lewis - Get in the Way - The Nashville Sit-Ins (PBS) 

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The Nashville Sit-Ins | John Lewis: Get in the Way | PBS LearningMedia

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As a college student, John Lewis learned the philosophy and the strategies of nonviolent direct action from his mentor, Rev. James Lawson. Lawson, Lewis, local ministers and students organized a sit-in campaign in 1960 at downtown Nashville lunch counters to challenge the legally sanctioned custom of denying service to African Americans.

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Ain't Scared of Your Jails (1960-1961) | Nashville Sit-Ins

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Ain't Scared of Your Jails (1960-1961) | Nashville Sit-Ins

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In 1960, Fisk student and activist Diane Nash recounts the lunch counter sit-ins in Nashville, Tennessee. From Eyes on the Prize: Ain't Scared of Your Jails (1960-1961).

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Eyes on the Prize
Clip: Season 1 Episode 3 | 1m 17s |

In 1960, Fisk student and activist Diane Nash recounts the lunch counter sit-ins in Nashville, Tennessee. From Eyes on the Prize: Ain't Scared of Your Jails (1960-1961).

Aired: 04/11/21

Expires: 03/14/25

Rating: TV-PG

Problems Playing Video? Report a Problem |

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Eyes on the Prize | Ain't Scared of Your Jails (1960-1961) | Nashville Sit-Ins | Season 1 | Episode 3 | PBS

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Activist Diane Nash recounts a day during the lunch counter sit-ins in Nashville.

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Courtesy U.S. Library of Congress (00651469)

The Nashville Sit-Ins were among the earliest non-violent direct action campaigns that targeted Southern racial segregation in the 1960s. The sit-ins, which lasted from February 13 to May 10, 1960, sought to desegregate downtown lunch counters in Nashville, Tennessee. The protests were coordinated by the Nashville Student Movement and the Nashville Christian Leadership Council (NCLC), primarily consisting of students from Fisk University, Baptist Theological Seminary, and Tennessee State University. Diane Nash and John Lewis, who were both students at Fisk University, emerged as the major leaders of the local movement.

On February 13, 1960, twelve days after the Greensboro, North Carolina sit-ins began, Nashville college students entered Kress (now K-Mart), Woolworth's, and McClellan stores at 12:40 p.m. After making their purchases, the students sat down at the lunch counters. Store owners initially refused to serve the students and closed the counters, claiming it was their "moral right" to determine whom they would or would not serve. The students continued the sit-ins over the next three months, expanding their targets to include lunch counters at the Greyhound and Trailways bus terminals, Grant's Variety Store, Walgreens Drugstore, and major Nashville department stores, Cain-Sloan and Harvey.

The first violent response to the protests came on February 27, which James Lawson, Jr., another protest leader called "big Saturday." The protesters that day were attacked by a white group opposing desegregation. The police arrested eighty-one protesters but none of the attackers. Those arrested were found guilty of disorderly conduct. They all decided to serve time in jail rather than pay fines.

As racial tension grew in Nashville, Mayor Ben West appointed a biracial committee to investigate segregation in the city. Despite the committee's numerous attempts at a compromise, the students declared that they would accept nothing less than the acknowledgement of their rights to sit at the store lunch counters along with white customers. On April 5, the committee suggested that the counters be divided into black and white sections. The NCLC and the Nashville Student Movement rejected the proposal, arguing that segregation of the counters was no better than black exclusion from them.

On April 19, a bomb destroyed the home of Z. Alexander Lobby, the defense attorney representing many of the protesters. The bombing of Lobby's home triggered a mass march to city hall where 2,500 protesters demanded answers from Mayor West. Diane Nash pointedly asked Mayor West if it was wrong for a citizen of Nashville to discriminate against his fellow citizens because of his race or skin color. The mayor admitted that it was wrong, giving the students an important symbolic victory in their campaign. Nash then asked the mayor if the lunch counters in Nashville should be desegregated. They mayor said they should.

After weeks of secret negotiations between merchants and protest leaders, an agreement was finally reached during the first week of May. On May 10, six downtown stores opened their lunch counters to black customers for the first time; the customers arrived in groups of two or three during the afternoon and were served without incident. With that agreement, Nashville became the first major southern city to begin desegregating public facilities. The Nashville campaign became a model for other civil rights protests in the 1960s and 1970s.

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Courtesy U.S. Library of Congress (00651469) The Nashville Sit-Ins were among the earliest non-violent direct action campaigns that targeted Southern racial segregation in the 1960s. The sit-ins, which lasted from February 13 to May 10, 1960, sought to desegregate downtown lunch counters in Nashville, Tennessee.

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Check out our MATH & NUMERACY TEACHING RESOURCES page.

Looking to organize your classes focused on student thinking and conceptual understanding?

Check out our INSTRUCTIONAL ROUTINES page, where you can learn about routines like Notice/Wonder, Same/Different, Slow Reveal graphs, visual patterns, and more.

Looking to help students build conceptual understanding and visual models?
Looking for interactive online activities for exploring math concepts?

Check out our page for suggestions on how to get started.

Looking for ways to learn more about teaching and learning in your adult math & numeracy classroom?

Check out our TEACHER-LED PROFESSIONAL DEVELOPMENT page.

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Adult Numeracy Network - Math & Numeracy Resources

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Check out our MATH & NUMERACY TEACHING RESOURCES page. Looking to organize your classes focused on student thinking and conceptual understanding? Check out our INSTRUCTIONAL ROUTINES page, where you can learn about routines like Notice/Wonder, Same/Different, Slow Reveal graphs, visual patterns, and more. Looking to help students build conceptual understanding and visual models?

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Evaluation for 2024 ANN Teaching & Learning Institute

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Evaluation for 2024 ANN Teaching & Learning Institute

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Please complete our evaluation before you leave. Any feedback is appreciated.

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2024 ANN Teaching & Learning Institute Evaluation

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Responses are anonymous and will be used to improve future institutes and training events.

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Math & Numeracy Strand Workshops at 2024 COABE

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Math & Numeracy Strand Workshops at 2024 COABE

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2024 COABE Math and Numeracy Strand and T&L Institute_v3

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ANN Collection of Instructional Routines

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ANN Collection of Instructional Routines

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"Instructional routines are specific and repeatable designs for learning that support both the teacher and students in the classroom... enabling all students to engage more fully in learning opportunities while building crucial mathematical thinking habits." Kelemanik, Lucenta, & Creighton (2016)

The Instructional Routines on this page are accessible and challenging to all students, can be approached in multiple ways using different types of sense-making strategies, promote understanding through discussion, make student thinking visible, make math visual and encourage practice of mental math

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"Instructional routines are specific and repeatable designs for learning that support both the teacher and students in the classroom... enabling all students to engage more fully in learning opportunities while building crucial mathematical thinking habits."

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Toolkit for Mathematics in Context: The Pedagogy of Liberation

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Toolkit for Mathematics in Context: The Pedagogy of Liberation

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Toolkit for “Mathematics in Context: The Pedagogy of Liberation”

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This toolkit will help educators consider how to “humanize math” using Learning for Justice’s Social Justice Standards. It provides opportunities for reflection and examples of real-world applications.

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It was in my process of learning to teach elementary math methods that I also learned about the Rights of the Learner. Olga Torres, a well-known and respected bilingual elementary teacher and teacher educator in Arizona, wanted to create a space for her third grade students to feel safe when learning math, but she needed a reminder for them each time they stepped into the risky space of knowing that you don't yet know everything. So Torres came up with the Rights of the Learner. Initially, I learned the rights were: 1. to be confused, 2. to make mistakes, 3. to say what makes sense to you, and 4. to write what makes sense to you.

But over time, those rights have evolved, both for her and for me. Now we agree that our RotL 2.0 could be: 1. to be confused, 2. to claim you've made a mistake and to revise your thinking, 3. to speak, listen, and be heard, and 4., to write, do and represent what makes sense to you. What I love about these new rights is that they are more inclusive and expansive. These rights start with the premise that ALL kids come with knowledge and teachers must first begin with that assumption. The RotL argue that what kids and teachers say about a math problem might not be the same, but that shouldn't discount what kids say just because it isn't what we as teachers expected them to say or it isn't what is written in the solution guide in the back of the book. The RotL fundamentally shifts the power from teacher to student. It claims that in this classroom, there is an agreed upon set of principles that we will honor and follow. Principles that should be granted to EVERYONE. EVERY TIME. EVERYWHERE.

Many who are reading this might say "but what do these rights have to do with math? with assessing children's thinking about math as they are learning?" Great point. Glad you asked, hypothetical person somewhere in the world. Teachers learn about what their kids know and have left to learn through the practice of assessment. They can assess children's thinking after the conclusion of a long unit/theme/large grouping of standards/year (summative assessment) or they can assess children's thinking in the moment with a much shorter time frame (formative assessment) ( Black and Wiliam, 1998). But there are two other types of assessment: convergent and divergent (Pryor and Croussard, 2008). Convergent Formative Assessments ask " IF the learner knows, understands or can do a predetermined thing" whereas DIVERGENT formative assessments ask "the learner knows, understands or can do" (Pryor & Crossouard, 2008, p.5). Another way to think of this difference is to ask yourself these questions:

1. Can my students give me an answer to a task that I haven't already predetermined PRIOR to the task?

2. Can my students give multiple solutions or methods of communicating their thinking?

3. Can I ask supporting, clarifying, or extending questions (Jacobs & Ambrose, 2008) that help me to learn more about my students' thinking rather than just getting them to say the correct answer?

4. Can my students and I co-create experiences or activities that assess THEIR OWN thinking?

5. Do I see myself as a facilitator of my students' learning and not just a sign post to direct them to the "correct path" as outlined in my lesson plan?

6. Can my students utilize the notion of Rough Draft Talk (Jansen, Cooper, Vascellaro, & Wandless, 2017) to revise their thinking as they learn more about the topic?

If you answered YAAAAASSSS to these, you're probably using DIVERGENT formative assessments. And now you're ready to think more about the Rights of the Learner.

Welcome to the Rights of the Learner Swim Team. The water is just fine. Come on in and wade in the pool for a bit. You don't need to be an elite swimmer to learn a few swim strokes. Eventually you'll be diving off the high board soon. Bring your floaties and don't forget to put on sunscreen. The Texas sun can be brutal.
References
Black, P., & Wiliam, D. (2010). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 92(1), 81-90.

Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching Children Mathematics, 15(5), 260-266.

Jansen, A., Cooper, B., Vascellaro, S., & Wandless, P. (2016). Rough-Draft Talk in Mathematics Classrooms. Mathematics Teaching in the Middle School, 22(5), 304-307. doi:10.5951/mathteacmiddscho.22.5.0304

Pryor, J., & Crossouard, B. (2008). A socio‐cultural theorisation of formative assessment. Oxford Review of Education, 34(1), 1-20.

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It was in my process of learning to teach elementary math methods that I also learned about the Rights of the Learner. Olga Torres, a well-known and respected bilingual elementary teacher and teacher educator in Arizona, wanted to create a space for her third grade students to feel safe when learning math, but she needed...

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This collection of images includes the one we looked at together. And about 100 more. The site also has suggestions for teaching with Fraction Talks.

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SLIDES from the 2024 ANN Teaching & Learning Institute

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SLIDES from the 2024 ANN Teaching & Learning Institute

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Rights of the Learner - Rehumanizing Classrooms with Olga G. Torres (podcast episode)

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Rights of the Learner - Rehumanizing Classrooms with Olga G. Torres (podcast episode)

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Rehumanizing the classroom defined by Olga. She talks about how it’s important to convince students that they are capable of anything. That as teachers we need to support them in this belief. This requires constant vigilance - being in a state of discovery all the time and always looking for the human element, and interacting, watching, observing, and questioning and never losing sight of the humans around you (the students) and the specialness of each.

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Updated: Mar 17, 2021

Olga G. Torres has been a bilingual elementary educator for over 40 years and a mathematics educator for over 25 years. She works as a Mathematics Education Consultant with the Marilyn Burns Education Associates/Math Solutions . Olga has been the recipient of many awards, including the 1995 Presidential Award of Excellence in Mathematics and Science Education. She is a teacher leader for CEMAL (Center for Mathematics Education of Latino/as), where she works with Dr. Marta Civil at the University of Arizona.

Karen worked with Olga last summer on an Equity in Education Webinar , in partnership with Casio Education and TODOS Math for All , where Olga shared her "Rights of the Learner" framework and talked about rehumanizing the math classroom, so though it would be a wonderful experience to have Olga join us and share more about her framework and her diverse teaching experiences that support equity in education.

Rehumanizing the classroom defined by Olga. She talks about how it's important to convince students that they are capable of anything. That as teachers we need to support them in this belief. This requires constant vigilance - being in a state of discovery all the time and always looking for the human element, and interacting, watching, observing, and questioning and never losing sight of the humans around you (the students) and the specialness of each.

Olga shares her personal teaching experiences and how these experiences influenced her perspective on what students need and how teaching should include the Rights of the Learner . She talks about what classrooms look like that are and are not focused on rehumanizing. Humanized classrooms are active, their curriculum is engaging, connected, and made relevant to the students.

What's inside the episode

Strategies to help create this rehumanized way of learning, and how to help change, as a teacher, in spite of obstacles or constrained environments.

How creating a culture of interactivity and acknowledging the students' thinking and knowledge makes a difference in how students see themselves, and ultimately how they learn.

Insight into how teachers, through sharing their own story, can fight against the programmed curriculum and build their own confidence in teaching from a problem-solving approach, not a process approach.

Why teachers must be agents of change, fight against the 'fixed-mindset' of our current education system & change to a 'growth-mindset', which includes working with administrators, parents, and community.

After this episode, you will believe that "Mistakes are a CELEBRATION!!!"

Resources Mentioned:

Rights of the Learner Framework (©Olga Torres 2006)

Olga G. Torres has been a bilingual elementary educator for over 40 years and a mathematics educator for over 25 years. She works as a Mathematics Education Consultant with the Marilyn Burns Education Associates/Math Solutions . Olga has been the recipient of many awards, including the 1995 Presidential Award of Excellence in Mathematics and Science Education. She is a teacher leader for CEMAL (Center for Mathematics Education of Latino/as), where she works with Dr. Marta Civil at the University of Arizona.

Karen worked with Olga last summer on an Equity in Education Webinar , in partnership with Casio Education and TODOS Math for All , where Olga shared her "Rights of the Learner" framework and talked about rehumanizing the math classroom, so though it would be a wonderful experience to have Olga join us and share more about her framework and her diverse teaching experiences that support equity in education.

Rehumanizing the classroom defined by Olga. She talks about how it's important to convince students that they are capable of anything. That as teachers we need to support them in this belief. This requires constant vigilance - being in a state of discovery all the time and always looking for the human element, and interacting, watching, observing, and questioning and never losing sight of the humans around you (the students) and the specialness of each.

Olga shares her personal teaching experiences and how these experiences influenced her perspective on what students need and how teaching should include the Rights of the Learner . She talks about what classrooms look like that are and are not focused on rehumanizing. Humanized classrooms are active, their curriculum is engaging, connected, and made relevant to the students.

What's inside the episode

Strategies to help create this rehumanized way of learning, and how to help change, as a teacher, in spite of obstacles or constrained environments.

How creating a culture of interactivity and acknowledging the students' thinking and knowledge makes a difference in how students see themselves, and ultimately how they learn.

Insight into how teachers, through sharing their own story, can fight against the programmed curriculum and build their own confidence in teaching from a problem-solving approach, not a process approach.

Why teachers must be agents of change, fight against the 'fixed-mindset' of our current education system & change to a 'growth-mindset', which includes working with administrators, parents, and community.

After this episode, you will believe that "Mistakes are a CELEBRATION!!!"

Resources Mentioned:

Rights of the Learner Framework (©Olga Torres 2006)

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S2 EP5: Rights of the Learner - Rehumanizing Classrooms with Olga G. Torres

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Olga G. Torres has been a bilingual elementary educator for over 40 years and a mathematics educator for over 25 years. She works as a Mathematics Education Consultant with the Marilyn Burns Education Associates/Math Solutions. Olga has been the recipient of many awards, including the 1995 Presidential Award of Excellence in Mathematics and Science Education.

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The SPLAT! routine uses Dot Talks to develop a visual and intuitive model for solving equations.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

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Splat! - Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

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Rehumanizing Schools: The Rights of the Learner - Olga Torres

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Rehumanizing Schools: The Rights of the Learner - Olga Torres

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In this joint webinar between Casio Education and TODOS Math for All, Olga Torres shares ways in which we can rehumanize the classroom and focus on the rights of the learners. She shares her philosophy of listening to what students know and helping use that to discover learning. She provides examples of what this might look like in a math classroom and inspires educators to listen to their students.

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Equity in Education Webinar Series:   Rehumanizing Schools - Rights of the Learner

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ANN Racial Equity in Math Education Committee

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ANN Racial Equity in Math Education Committee

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The ANN Racial Equity in Math Education committee meets on the fourth Tuesday of every month. Click here to learn more and register for upcoming meetings.

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ormed during the writing of the , this working group focuses on education and action to promote equity in our classrooms, teaching practice, and organization.

The work of the ANN Racial Equity in Math Education Committee centers on three questions: Where does racial inequity show up? How does it affect our students? How can we disrupt it?

High-quality mathematics instruction requires that practitioners acknowledge and address that systems steeped in white supremacy, our own learned biases, and the history of math education all contribute to dehumanizing mathematics education for teachers and students.

We work to live in the community value of rehumanizing mathematics education through the disruption of racial inequity. We center our humanity and the humanity of our students as we imagine what this could look like.

We offer and promote opportunities for teachers to be learners and to have and model mathematical habits of mind like being comfortable not knowing, investigating, and appreciating and learning from mistakes in the context of racial equity in math education. We will work toward our members feeling empowered to contribute to discourse around racial equity in math teaching and learning.

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Adult Numeracy Network - Racial Equity in Math Education Committee

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ormed during the writing of the , this working group focuses on education and action to promote equity in our classrooms, teaching practice, and organization. The work of the ANN Racial Equity in Math Education Committee centers on three questions: Where does racial inequity show up? How does it affect our students?

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Do math every month with Community of Adult Math Instructors (CAMI)! 

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Do math every month with Community of Adult Math Instructors (CAMI)! 

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CAMI is a math teachers circle that meets online once a month for teachers to learn math together

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Community of Adult Math Instructors (CAMI)

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Today we looked at a problem involving rebounding balls on a billiard table.

The rules of our problem:

A "table" can have different dimensions (measurements of height and width).

A "ball," modeled by a straight line, is launched at 45 degrees from the bottom left corner of a table.

Continue reading "Billiards!"
We started this meeting with a warm-up question: What is something you are good at that you could teach someone else? It turned out we were a very talented group with skills ranging from kayaking to mountain climbing and from making enchiladas to reading and writing Egyptian hieroglyphs.

We took some time on our own to explore some demonstrations of the new music and sound features of Mathigon Polypad. (To learn more, go to Using Polypad: Music - Mathigon.)

Continue reading "Music and Polypad"

In this meeting, Amy introduced the story table, which is a teaching tool for solving algebraic equations. Story tables allow us to use guess and check and then analyze patterns in the results, in order to find values of x that make equations true.

To get us started, Amy shared the following algebraic equation:

And asked us to tell the story of x. To find a solution in this story, Amy asked us for the moment not use other ways of solving equations.

Continue reading "Story Tables"

Sarah and Eric have been teaching themselves how to code using Javascript, CSS, and HTML. The What Comes Next? game is the result of more than a year's work. We are not fast coders! We used this meeting to share our game and to see if teachers might use it with their students.

To play the game: What Comes Next?

Continue reading "What Comes Next?"

For the last CAMI meeting before the 2022 summer break, we explored and created hanger diagrams. The session began with a notice and wonder of this hanger.

Continue reading "Hanger Diagrams"

Cindy Aossey and Dee Crescitelli started the session with a notice and wonder about two graphs.

Continue reading "Graceful Labeling of Graphs"

From MoMath Mindbenders for the Quarantined

Cindy started the meeting by asking participants to draw rectangles in Jamboard using the graph paper background.

Tip: To make a straight line in Jamboard, hold down the shift key!

Initial exploration in Jamboard

Continue reading "MoMath Area and Perimeter Puzzle"

The session started with an example of Egyptian representations of whole numbers.

Continue reading "Egyptian Fractions"

In our first meeting of fall 2021, Sarah and Amy led through the group through an exploration of the ways of cutting a shape into pieces.

Continue reading "Representing Fractions"

For the May afternoon CAMI meeting, we considered the case of the tethered goat. We observed goats tethered to fences and barns of various shapes and sizes and considered the grazing area of the goats under various conditions.

Continue reading "Stubborn as a Goat"

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Community of Adult Math Instructors (CAMI)

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Today we looked at a problem involving rebounding balls on a billiard table. The rules of our problem: A "table" can have different dimensions (measurements of height and width). A "ball," modeled by a straight line, is launched at 45 degrees from the bottom left corner of a table.

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NCTM (National Council of Teachers of Mathematics)

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NCTM (National Council of Teachers of Mathematics)

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ANN is an affiliate member of NCTM.

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Benefits of Membership - National Council of Teachers of Mathematics

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Membership is designed to meet the needs of those reaching students, including teachers, administrators, specialists, coaches, teacher-educators, and others.

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Join the LINCS Math & Numeracy Community of Practice

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Join the LINCS Math & Numeracy Community of Practice

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LINCS Community | Adult Education and Literacy | U.S. Department of Education

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The group is a community of practice where practitioners, advocates, researchers, learners, policymakers, and others discuss mathematics and numeracy issues in adult education, including research and evidence-based practices, instructional strategies, and resources.

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ALM is the Adults Learning Mathematics network (European/worldwide) and affiliated with ANN.

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One adult education teacher's experience with WODB

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Which One Doesn't Belong? (WODB) is a website with a very simple concept. It is "dedicated to providing thought-provoking puzzles for math teachers and students alike". Basically, it presents four of something and you have to come up with a reason why each one of the four things doesn't belong. But it is far more than a collection of brain teasers.

One way we can help students develop different ways of thinking in math is to have them work on activities where they have to classify mathematical objects. In working on these kinds of tasks, "Learners devise their own classifications for mathematical objects, and apply classifications devised by others. They learn to discriminate carefully and recognize the properties of objects. They also develop mathematical language and definitions".[1]

WODB is a great resource for bringing this kind of rich, classification activity to students. The site is divided into three main categories - Numbers, Shapes and Graphs.

I started off with the Numbers section because it fit better with what we were doing in class. I decided to try out a few of the WODB puzzles with my class of adult education/HSE students as a warm-up to start class.

I gave out the following puzzle as an example to begin and we did it together as a "think aloud" so they could be clear on how the puzzles work.

As we talked though it, interesting things started to come out immediately. One student said, "I know 3 and 27 are both part of the three times table, and I know 31 isn't, but I'm not sure about the 123. I don't think it is." Another student asked how she knew the 31 was not "part of the three times table" and she said, "Because I know that 30 is, because it goes 27, 30, 33, so it skips the 31". Then another student had some memory of a divisibility rule for 3 (add up all the digits and see if it's a multiple of 3) and we tried it with some numbers we knew were multiples of 3 and then we tried it on the 123. Then someone suggested we check and divided 123 by 3 to see if it came out evenly. All of that reasoning and calculation, just to make an observation about one of the numbers (the 31). I made sure to offer "9 is the only single digit number" and "123 is the only three digit number" as potential answers to help less confident students realize that any differences they saw were acceptable.

Once they all seemed clear on what to do, I put the following puzzle up on the board and asked them to come up with one quality that made each number different/unique compared to the other three.

Here's the first one I gave students to work on their own:

The way I set up the activity was to draw the square pictured above on the board and have students copy it in their notebook and write the differences around it. Then as we went over it one number at a time, I had a few volunteers share what they observed. One math practice that came up immediately was the use of precision in explaining mathematical ideas. With me as the note-taker, I was able to encourage students to clarify their statements by asking other students to say it in their own words. When someone else understood something different from what they meant, we worked together to make the statement more precise. The next time I do this activity I think I will have the students come up and write their observations themselves.

Here's what my students came up with:

The first thing that attracted me to the exercise was the way students at all different levels could approach the problem. There are so many different and correct ways to describe what makes each number unique that every student was engaged. As I walked around and looked at students filling the margins with calculations & observations and talking to their neighbors, I saw how effectively this activity could develop student fluency and comfort with numbers. I liked the approach of the student who said, "If you divide 16 by 2 it is the only one without a remainder". They didn't look at it and say "16 is the only even number", but they were just playing around with the numbers and were curious as to what would happen if they divided each of them by 2. Then, with their observation up on the board, we talked about it a bit and connected it to the idea of even numbers.

Along similar lines, sharing observations was a great opportunity to introduce some vocabulary. In the board work above you can see that for 43, one student observed "No number can be multiplied by itself to get 43". Which was a nice place to introduce " perfect squares ", which many of them recognized but did not know the words for.

Here's the second one we did:

And here's what students came up with:

We didn't get to as many different observations for the second one, in part because it was second, but also because we had such a rich conversation about the first number we discussed. I started with the 17 and one student said, "It is the only one you can't multiply anything to get". We spent some time unpacking that (clarifying what he meant; coming up with the two numbers that can be multiplied to get 17 - 1 and 17; testing to be sure that was not true of the other numbers). Students were curious about this strange phenomenon of a number that "you can't multiply anything to get" and it was a great way to start talking about prime numbers - a vocabulary word I introduced after all of our unpacking, along with composite.

To give you a sense of the richness of the offerings, I'm including some samples from the Shapes and the Graph sections, which work the same way - you have to find a reason why each one doesn't belong in the set - but with shapes and graphs.

Here are a few selections from the Shapes section:

Here are a few samples from the Graph section:

As I wrote, I used this as a warm-up at the beginning of class. After we finished up, I asked students to reflect on the activity and they all said or agreed with some version of the statements "It was interesting", "It was challenging but not too hard" and "You really had to think about the numbers in different ways".

A few of them asked where they could find more puzzles like these and I gave them the website to explore on their own. Several said they would try it out with their kids and report back on how it goes.

Please write a reply below and let me know what you think.

How do you think students can benefit from categorizing numbers/shapes/graphs in this way?

Would you try this with your students? Why or why not?

Try one with your students and let us all know how it goes.

Thanks for reading!

[1] Swan, Malcolm., 2005. Improving Learning in Mathematics: Challenges and Strategies Department for Education and Skills

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Learning through classification: What makes this number (or shape or graph) different from the others?

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Which One Doesn't Belong? (WODB) is a website with a very simple concept. It is "dedicated to providing thought-provoking puzzles for math teachers and students alike". Basically,...

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PADLET: Where are you from? Where do you belong?

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PADLET: Where are you from? Where do you belong?

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Which One Doesn't Belong? (WODB) Collection

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Which One Doesn't Belong? (WODB) Collection

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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Steve Wybourney: "Provide Space to Notice"

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Steve Wybourney: "Provide Space to Notice"

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Give students several copies of the same image - along with ample space to notice - and they will amaze you. In this post, you'll be taken on a tour of noticing. At the end of the video, you'll find a page which you can download and use with your students. I encourage you to show the video to your class, pause it at the strategic point I've indicated in the recording, and then give your students massive space to notice. When you are finished, if you have an opportunity, send me a picture of the student thinking that emerges in your classroom. I'd love to post several of those pictures to the blog.

To download the PDF described in the video, simply click on the link below.
Download the Massive Space to Notice Dot Pattern.
A similar post that may interest you is " 8 Animated Dots and 1 Powerful Question."

You may also enjoy the post Stepping Into Each Other's Classrooms or the animated series which describes some strategies to make it happen: The Animated Learning Walks Series.

In upcoming posts, I'll detail how to quickly and easily make several dot patterns, such as the one in the video. If you are interested in a jump start on that concept, I encourage you to take a quick look at How to Make Quick Subitizing Images + 3 Free Resources.
Further Notes
I'm impressed by these responses from Matt Hardman's (@mdhardm) students in Georgia. I hadn't thought to adjust the orientation to see more possibilities, but as soon as I saw what Matt's students had done, I immediately learned something new. Thank you for sharing these pictures!

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Provide Massive Space to notice - Steve Wyborney's Blog: I'm on a Learning Mission.

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Give students several copies of the same image - along with ample space to notice - and they will amaze you. In this post, you'll be taken on a tour of noticing. At the end of the video, you'll find a page which you can download and use with your students.

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Steve Wybourney: 180 Opportunities to Notice

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Steve Wybourney: 180 Opportunities to Notice

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Steve Wyborney's Blog: I'm on a Learning Mission.

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180 Opportunities to Notice - Steve Wyborney’s Blog: I’m on a Learning Mission.

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In my previous post, Provide Massive Space to Notice, I described how to repeatedly use the same dot pattern to promote noticing. In this post, I would

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What values are important to you? How can that value help you learn math?

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What values are important to you? How can that value help you learn math?

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I first did this writing assignment after reading an article called Social-Psychological Interventions in Education: They are Not Magic. The article is essentially a literature review, describing brief activities that target students' thoughts, feelings, and beliefs in and about school. The activities do not teach students academic content but instead target students' psychology, such as their beliefs that they have the potential to improve their intelligence or that they belong and are valued in school.

I've attached a handout that I use with students. The basic process is to have students choose three values that are important to them from a list (and they can add their own if they want). They then focus on one of those values and write about why it is important to them. Then they write about how the value they choose can help them in math class.

It is telling that there is usually at least one student who responds to the writing prompt by saying, "Isn't this math class?" The implication being that values are not important in learning math.

I disagree.

Values are something that we can lean on when we struggle. They can give us strength. They are important to bring with us into the classroom and keep in mind when we challenge ourselves.

I have used students writing in different ways. Sometimes students read them out, sometimes they share with a partner. Sometimes I collect them and write each student a letter in response. Sometimes I collect them and put each of them in an envelope with the student's name on it - then I hold it until the end of the semester, or the halfway point and have them write a response. Sometimes I hold them and give them back a few times over the course of a semester and ask students to keep writing about how that value is impacting their learning in math, using specific examples from class.

The activity's ability to positively impact students sense of self in class feels intuitively correct to me, but I used it because the article cites two-studies, one with low- and middle- income black and white 7th grade students and the other with men and women in a college physics class. The results in both were the same - one or several 15-20 minute writing sessions in the beginning of the year led to reductions in the grade gap between the black and white 7th grade students and between the men and women in the physics class.

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What values are important to you? How can that value help you learn math?

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I first did this writing assignment after reading an article called Social-Psychological Interventions in Education: They are Not Magic. The article is essentially a literature review, describ...

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Christopher Danielson blog on Students' Sense of Belonging and WODB

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Christopher Danielson blog on Students' Sense of Belonging and WODB

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Pierre Tranchemontagne's Collection of Dot Talks

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Pierre Tranchemontagne's Collection of Dot Talks

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​​"Give students several copies of the same image - along with ample space to notice - and they will amaze you." Steve Wyborney (@SteveWyborney)

See the Re(s)sources section for more info on how to go about using the following images.​..

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​​"Give students several copies of the same image - along with ample space to notice - and they will amaze you." Steve Wyborney ( @SteveWyborney ) See the Re(s)sources section for more...

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Editable(and edible) Dot Talks & Number Talk Images from Berkeley Everett

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Editable(and edible) Dot Talks & Number Talk Images from Berkeley Everett

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Join us tonight for dinner at 6PM! RSVP HERE

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Join us tonight for dinner at 6PM! RSVP HERE

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You're Invited! ANN Dinner After the Teaching & Learning Institute (March 17, 2024 6:00pm)

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Come join your ANN friends for dinner at Romano's Macaroni Grill at 6:00 pm on Sunday, March 17th, after the ANN Teaching & Learning Institute. Everyone will need to buy their own food and drinks, but we will make a reservation for the whole group so that we can all sit together.

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Instantly built a devoted audience of children and adults who fell in love with the game's beautiful, colorful display, and connection with deep mathematical understanding.

Honestly, this has got to be one of the most engaging and effective ways of introducing the idea of primes being the 'building blocks' of numbers and building other general logic skills... Overall, Prime Climb is an incredibly flexible game, and certainly met the high expectations it set itself.

This game blew my mind! It blew my wife's mind, it blew my kid's mind... it is one of the coolest visualizations of mathematics and prime numbers I've ever seen ever. It is awesome!

Take a look at Prime Climb, an excellent new game... perfect for adults and children alike.

This game is so rich in mathematical ideas that I literally spent a week investigating it with my class.

Rated #1 Educational Math Game!

Prime Climb is an excellent way to teach about prime numbers, factors, common multiples, and that math is fun!... I loved how Prime Climb engaged my math loving kids and my kids who tolerate math. It was engaging and challenging enough that no one was bored, but easy enough to understand that no one was frustrated. It was the perfect balance. (It was fun for the adults as well.)

This is an amazing game! It is genius actually. You can play this with both young and old and adapt it to anyone's ability. Players must not only use their math skills but their strategy skills as well. I believe this game should be in every classroom in America as well as every home!!

For a game that is a relatively pure experience of math equations, I think you'll be surprised how much fun it can be for players of all ages.

A fun and simple way to bring multiplication, division, and prime numbers all in one easy to play game. Awesome!

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Math for Love is devoted to transforming how math is taught and learned. Offering a free lesson library, plus games, summer curriculum, and more.

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How to Add More Play to Your Grown-Up Life, Even Now

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How to Add More Play to Your Grown-Up Life, Even Now

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The Math Practitioner Newsletter: Summer 2023

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The Math Practitioner Newsletter: Summer 2023

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Use addition, subtraction, multiplication, and/or division with each
number once to determine if the answer is True or False. 6, 4, 3 = 8
​

If you found this problem an interesting and
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You can count on our collection of hands-on math materials to enhance your students' learning experience.

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New Readers Press improves adult learners’ literacy and life skills with ESL, ABE, and HSE learning materials for reading, writing, math, science, and more.

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Crazy Eights (DESMOS): Matching Dots to Expressions

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Crazy Eights (DESMOS): Matching Dots to Expressions

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A "mash-up" of a card sort and number talks for dot diagrams with eight dots. The activity can easily be modified to include different diagrams and/or different numbers of dots . . . of course, then you would need to change the title as well!

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Christopher Danielson on his book, Which One Doesn't Belong?

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Christopher Danielson on his book, Which One Doesn't Belong?

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Christopher Danielson: Which One Doesn't Belong?

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"Oh, wow! This is going to be fun!" As a parent, Christopher Danielson (Which One Doesn't Belong?) was thrilled with the opportunities for rich discussion afforded to his family through narrative text. But when it came to shapes books... not so much. H

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Edit this template to add your own Which One Doesn't Belong Problems.

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Hundreds of Challenging Math Problems Worth Solving

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Hundreds of Challenging Math Problems Worth Solving

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A review of Open Middle's collection of problems, by an adult education math teacher for adult education math teachers.

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The Mathematical Practices that are in the College and Career Readiness Standards for Adult Education define what it means to be a mathematically proficient student. As adult education instructors, our job is to help our students navigate over the swells in the tempest of their angst until they get to the point where they have enough confidence in their own abilities to weather the sea of mathematics.

Consider the first standard, It explains that our students should be able to approach a math problem or situation - something a bit challenging that they might never have seen before - and find a way into solving it. They should be able to develop flexibility with numbers and the ability to approach problems with the understanding that there are multiple pathways that can lead to a solution. They should have confidence that if they stick with it long enough, they can find an appropriate strategy that will solve the problem. That means that we, as their teachers, need to provide intriguing math problems that catch our students' attention and then nourish and celebrate the different methods of problem solving that our students intuitively gravitate towards. MP1: Make sense of problems and persevere in solving them. ( Mathematical Mindsets, Jo Boaler, 2016)

One resource I strongly recommend for these kinds of math problems is Open Middle . As of this writing, there are over 300 high-interest problems housed at the website. They are organized by grade level and topic that make it easy to zero in on a particular skill level and area of focus that you want to bring into your classroom.

So what makes a problem open-middle?

The website explains:

They have a "closed beginning" meaning that they all start with the same initial problem.

They have a "closed end" meaning that they all end with the same answer.

They have an "open middle" meaning that there are multiple ways to approach and ultimately solve the problem .

Problems with Multiple Solution Methods

As an example, consider the following problem. At first glance this may seem pretty straightforward, requiring only a knowledge of the rules of subtraction in order to solve it

Each problem comes with a hint. For this problem the hint is: Remember that zeros are not allowed. Because you can only use each digit once, the digit in the hundreds place can't be the same.

Try solving it yourself before looking at the student solutions listed below. Keep in mind that there is one optimal answer to this problem albeit multiple ways to arrive at this solution.
(To find this and other subtraction problems - Open Middle Subtraction)
This is listed under Grade 2, so keep this in mind when navigating the website. Don't necessarily start with high-school level if your students need the basics in algebraic thinking and are just beginning to learn how to be flexible with numbers . If you've already worked out a solution to the problem, read on to see examples of how my students approached this.

Notice that one student did not arrive at the optimal answer on his first try. He was a tad disappointed when he saw that a classmate had found a smaller difference until I asked him if there might be another combination of numbers, besides what his peer had already found, that might lead to the optimal answer of 14. This led to a flurry of renewed interest in the problem as all students, even those whose calculations had already led to 14, busied themselves in trying to discover what other number combinations would work. Two of those solutions are pictured above, which clearly indicate a pattern that can lead to additional solutions.

To wrap up this activity, have each student who discovered the optimal answer of 14 explain how they arrived at their answer. When all solutions that students found are placed on the board, ask students what they noticed about the pattern that is evidenced in the solutions. If they have not already found and commented on the pattern in the combinations of numbers that work, ask students if they see any patterns in the solutions and discuss how the pattern changes with each equation. Recognizing patterns and developing flexibility with numbers go a long way in helping our students to become mathematically proficient.

Problems with Multiple Solutions

Some of the problems on the website are also open-ended in that there are multiple, sometimes infinite, answers to the problem. Students may still arrive at their answer via multiple solution pathways, but now everyone in the class has the ability to create and defend their own unique math situation. Table of Values: Function is one such example, which simply asks students to create a table of values that represents a function.

Similarly, there is a problem called Table of Values: Not a Function.

These activities can reinforce the basic definition of a function. Many times we focus our instruction on finding the rule of a function when we present a table of values to our students, but it's also important that they are able to look at an input/output table, a graph, a range and domain set with arrow notation, or sets of ordered pairs and correctly identify which ones represent a function and which ones do not.
(To find these and other function problems - Open Middle Functions)
There may be no readily apparent rule for a set of values that our students might see on an HSE exam, other than it is or is not a function based on the definition of a function: a relationship between two values where each input value has only one unique output. While having an understanding of this rule is a procedural skill, requiring students to create their own set of values using their choice of an input/output table, graph, range and domain set with arrow notation, or sets of ordered pairs, requires a higher depth of knowledge, especially if students are subsequently tasked to create a real-life scenario that their function represents. Students are more apt to remember the basic definition of a function if they have engaged in this kind of an open-ended activity.

Whenever you are planning a unit on a particular math topic, it is well worth visiting Open Middle. There is such a wide range of problems, you are sure to find something to engage your students and teach them that they are capable of creative problem-solving.

Explore the site and then take a minute or two to add a comment below.

Let us know what problems you use and how they go with your students.

This review of Open Middle o riginally appeared in the Spring 2017 issue of The Math Practitioner which can be downloaded here. This issue includes a printable version of an Open-Middle problem, Create Squares. The review has been modified to reflect the style of the reviews at CollectEdNY.

The Math Practitioner is a newsletter published by The Adult Numeracy Network (ANN) for teachers of adult numeracy and high school equivalency math.

If you are interested in receiving this newsletter on a regular basis, please our national community of adult education math practitioners at the ANN website .

ANN is a community dedicated to quality mathematics instruction at the adult level. We encourage collaboration and leadership, and would like to hear about what you are doing in your classroom to help your students reach their goals in mathematics. We're also interested in your "aha" moments as an adult education instructor. To that end, we encourage submissions of articles, activities, and other items of interest related to math for adult learners for consideration for our newsletter. Please direct all correspondence regarding The Math Practitioner to: Patricia Helmuth, mathpractitioner@gmail.com .

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Hundreds of Challenging Math Problems Worth Solving

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The Mathematical Practices that are in the College and Career Readiness Standards for Adult Education define what it means to be a mathematically proficient student. As adult education instructors,...

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How Does this Belong? (a variation on Which One Doesn't Belong?) - DESMOS

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How Does this Belong? (a variation on Which One Doesn't Belong?) - DESMOS

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By Christine Koerner

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How Does this Belong? (a variation on Which One Doesn't Belong?)

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This variation of WODB was inspired by the work of https://twitter.com/teachnext_tmb and specifically this Twitter thread - https://twitter.com/teachnext_tmb/status/1391109941675573251?s=20

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Index - National Council of Teachers of Mathematics

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Open Middle: A Review from The Math Practitioner

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Open Middle: A Review from The Math Practitioner

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Sit-ins: Nashville, Tenn. - Civil Rights Digital Library

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Sit-ins: Nashville, Tenn. - Civil Rights Digital Library

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Some content (or its descriptions) found on this site may be harmful and difficult to view. These materials may be graphic or reflect biases. In some cases, they may conflict with strongly held cultural values, beliefs or restrictions. We provide access to these materials to preserve the historical record, but we do not endorse the attitudes, prejudices, or behaviors found within them. Read more

The Digital Library of Georgia is part of the GALILEO Initiative and located at The University of Georgia Libraries
© 2024 Digital Library of Georgia

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Some content (or its descriptions) found on this site may be harmful and difficult to view. These materials may be graphic or reflect biases. In some cases, they may conflict with strongly held cultural values, beliefs or restrictions. We provide access to these materials to preserve the historical record, but we do not endorse the attitudes, prejudices, or behaviors found within them.

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Playlist of songs recorded in Nashville, TN

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Playlist of songs recorded in Nashville, TN