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Number Talks Recordings in Distance Learning

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Number Talks Recordings in Distance Learning

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Number Talks in Distance Learning Videos 20-21

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Scores for Latino students more than doubled at Robbins Elementary since 2014-15.

Sydney Johnson

Sydney Johnson

California school districts have long struggled with a persistent gap in math test scores between racial and ethnic groups. But at one small rural school district, the gap between Latino and white students has narrowed more than it has at most districts in the state.

At Winship-Robbins Elementary School District, a single-school district in south Sutter County, the percentage of Latino students meeting or exceeding standards on the Smarter Balanced math test more than doubled over the last five years. And although their scores still slightly trail those of their white peers, the gap between them has narrowed by nearly 16 percentage points during that time.

One of the main reasons for the improved scores is a change in the way teachers talk to their students about math, said officials at Robbins Elementary, the district's one school. Starting last school year, teachers focused on creating more opportunities for students to talk through word problems with each other and build their ability to recognize and apply math terms, rather than relying on rote memorization.

The shift has made math at Robbins Elementary more social - and that's intentional. During a recent morning math lesson, students in Mayra Medina's 6th-grade math lesson were buzzing with group discussion about how scaling shapes up and down relates to size and proportion.

"If students aren't talking about their math learning, they won't have retention," said Kim Richter, curriculum and instruction coordinator for Winship-Robbins Elementary School District. "Our English learners particularly need that opportunity to think and read out loud and collaborate with a partner who can support them."

In the spring of 2015, California began administering Smarter Balanced assessments, annual standardized tests in math and English language arts aligned with the Common Core standards. Last school year, 39.7 percent of all California students met or exceeded state standards in math, an increase of about 1 percentage point from the year before.

While the average statewide math score was low, the scores for some student groups were even lower. Statewide, the scores of Latino and African-American students on the Smarter Balanced math test trailed those of their white and Asian peers, a chronic pattern known as the achievement gap. California adopted the Common Core standards in 2010 in part to close that gap and the changes Robbins Elementary teachers made as they implemented them point to practices that might be working.

Nestled between rivers and farmland north of Sacramento, Robbins Elementary serves about 120 students in grades K-8. Overall, nearly 80 percent of the overall student population is Latino. And about 4 in 5 students at the school are low-income, according to data from the Department of Education. About 40 percent are English learners and many others speak a language other than English at home, including Spanish, Russian and Arabic, according to Dawn Carl, principal and superintendent.

Creating more opportunities to share out loud and learn from one another while solving math problems is intended to support students from all language backgrounds, Richter said, not only the school's English learners. But many factors beyond the classroom create difficult hurdles for the school's low-income students.

"Our town is poor and rural. We don't have a public library and many of our students don't have internet at home," she added. "We have a store where you can buy beer and bait, but you can't buy fresh vegetables."

The new Common Core math standards require significant shifts in instruction, such as emphasizing math concepts over memorizing facts and procedures. After seeing a dip in math test scores a few years after the district began implementing the Common Core standards, staff met every other Wednesday last school year to review and refine its approach to math.

They noticed their math lessons were missing what Richter describes as "productive struggle," where students can work through challenging problems and mistakes, rather than providing each step and answer. "The rigor just wasn't there," she said.

Without the money to send teachers to professional learning events, teachers spent the afternoons working together through "Visible Learning," a book-based program with strategies for teachers to evaluate their own teaching practices. They also attended free math instruction workshops at UC Davis.

The work is starting to pay off. Among all students at the school, the number meeting or exceeding state standards for math went from 43 percent in 2017-18 to more than half last school year.

"By making sure we were teaching not only content but also academic language changed everything for us, especially our English learners," Richter said.

The new focus on language shows up in different ways. Medina started her recent math lesson by first introducing a word problem to students, who read the question out loud. Then students, who worked in groups of four, entered into a discussion about how they would solve the problem. After the students worked through their ideas, Medina then modeled how to approach the problem by walking through key steps. Finally, the students took turns sharing how they got to their answers.

"The way I learned, teachers would model how to solve a problem and there was a big focus on speed. But we didn't get a lot of time to work through problems together," Medina said. "This is much more collaborative-based learning. It prompts discussion so students can share strengths and experiences."

Also starting this year, each lesson has a language objective, or terms and phrases that students should know at the end of class. That is paired with a content objective, meaning the academic material that students should come away understanding and a social objective such as problem-solving with peers. Teachers outline the objectives for students during class and keep them visible on the whiteboard for reference.

"Every time we plan the objectives, we unpack the standards again and again," Richter said. "Before, it was easy for teachers to follow the book if they didn't know what they were doing. Now, they have to really get into the math concepts when lesson planning."

Medina said the Wednesday math meetings last year helped her learn how to facilitate discussions instead of giving students the answer. She also learned ways to integrate math vocabulary more seamlessly in lessons by letting students know when they are practicing mathematical concepts, such as ratios and proportional relationships.

Each morning, students who need extra help in math or writing also attend a small 30-minute class focused on those subjects. Every six weeks, staff review student performance data to determine if they need additional support, such as smaller breakout groups that focus on specific math concepts.

The school is still working through some lingering challenges. In January, the district purchased new math textbooks to better align with the shifts teachers were making in the classroom, and they are still getting familiar with the new materials.

And due to its small size, the school has uneven enrollment in grade levels, resulting in three classes that combine different grade levels at the school. Richter said, "It's hard to do this kind of specific instruction when you're dealing with two grades."

Since 2014-15, the first year of the Smarter Balanced test, the percentage of California's Latino students who met or exceeded standards on the math test increased from 21 to 28 percent, a larger rate of increase than the state's white and Asian students. However, a wide achievement gap persists.

"The gap for Latino students is still huge, and that's troubling," said Patricia Gándara, a research professor at UCLA and co-director the Civil Rights Project, a research and policy institute that analyzes racial inequities in public education.

The slight increase in math scores among Latino students could reflect positive trends in the economy, but it could also reflect negative trends in the student population, Gándara said.

"We have people leaving and being deported and the ones who leave are the ones who are most stressed," said Gándara, referring to students who experience trauma and threats of deportation and how that can impact academic performance. "That could change the composition of who takes the test."

Staff at Robbins say there's still more work to be done.

"It makes us proud that the things we have chosen to focus on are making a difference. But we aren't where we need to be yet," Richter said. "And we definitely aren't sitting back, that's for sure."
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Students talk through math in this California school. Now test scores are rising.

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Sydney Johnson Sydney Johnson California school districts have long struggled with a persistent gap in math test scores between racial and ethnic groups. But at one small rural school district, the gap between Latino and white students has narrowed more than it has at most districts in the state.

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The standards for mathematical practices are the same for K-12 grade. Many times teachers need to know “How do I teach practice #1 at my grade level. The link above shows examples of the math…

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From Stanford Online's "How To Learn Math for Teachers and Parents": Number Talks

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When schools started closing months ago, we heard two loud requests from teachers in our community. They wanted:

1. Written feedback for students.

2. Co-teacher access to student data.

Those sounded like unambiguously good ideas, whether schools were closed or not. Good pedagogy. Good technology. Good math. We made both.

Here is the new loudest request:

Self-checking activities. Especially card sorts.

hey @Desmos - is there a simple way for students to see their accuracy for a matching graph/eqn card sort? thank you!

Is there a way to make a @Desmos card sort self checking? #MTBoS #iteachmath #remotelearning

@Desmos to help with virtual learning, is there a way to make it that students cannot advance to the next slide until their cardsort is completed correctly?

Let's say you have students working on a card sort like this, matching graphs of web traffic pre- and post-coronavirus to the correct websites.

What kind of feedback would be most helpful for students here?

Feedback is supposed to change thinking. That's its job. Ideally it develops student thinking, but some feedback diminishes it. For example, Kluger and DeNisi (1996) found that one-third of feedback interventions decreased performance.

Butler (1986) found that grades were less effective feedback than comments at developing both student thinking and intrinsic motivation. When the feedback came in the form of grades and comments, the results were the same as if the teacher had returned grades alone. Grades tend to catch and keep student attention.

So we could give students a button that tells them they're right or wrong.

Resourceful teachers in our community have put together screens like this. Students press a button and see if their card sort is right or wrong.

My concerns:

1. If students find out that they're right, will they simply stop thinking about the card sort, even if they could benefit from more thinking?

2. If students find out that they're wrong, do they have enough information related to the task to help them do more than guess and check their way to their next answer?

For example, in this video, you can see a student move between a card sort and the self-check screen three times in 11 seconds. Is the student having three separate mathematical realizations during that interval . . . or just guessing and checking?

On another card sort, students click the "Check Work" button up to 10 times.

Instead we could tell students which card is the hardest for the class.

Our teacher dashboard will show teachers which card is hardest for students. I used the web traffic card sort last week when I taught Wendy Baty's eighth grade class online. After a few minutes of early work, I told the students that "Netflix" had been the hardest card for them to correctly group and then invited them to think about their sort again.

I suspect that students gave the Netflix card some extra thought (e.g., "How should I think about the maximum y-value in these cards? Is Netflix more popular than YouTube or the other way around?") even if they had matched the card correctly. I suspect this revelation helped every student develop their thinking more than if we simply told them their sort was right or wrong.

We could also make it easier for students to see and comment on each other's card sorts.

In this video, you can see Julie Reulbach and Christopher Danielson talking about their different sorts. I paired them up specifically because I knew their card sorts were different.

Christopher's sort is wrong, and I suspect he benefited more from their conversation than he would from hearing a computer tell him he's wrong.

Julie's sort is right, and I suspect she benefited more from explaining and defending her sort than she would from hearing a computer tell her she's right.

I suspect that conversations like theirs will also benefit students well beyond this particular card sort, helping them understand that "correctness" is something that's determined and justified by people, not just answer keys, and that mathematical authority is endowed in students, not just in adults and computers.

Teachers could create reaction videos.

In this video, Johanna Langill doesn't respond to every student's idea individually. Instead, she looks for themes in student thinking, celebrates them, then connects and responds to those themes.

I suspect that students will learn more from Johanna's holistic analysis of student work than they would an individualized grade of "right" or "wrong."

Our values are in conflict.

We want to build tools and curriculum for classes that actually exist, not for the classes of our imaginations or dreams. That's why we field test our work relentlessly. It's why we constantly shrink the amount of bandwidth our activities and tools require. It's why we lead our field in accessibility.

We also want students to know that there are lots of interesting ways to be right in math class, and that wrong answers are useful for learning. That's why we ask students to estimate, argue, notice, and wonder. It's why we have built so many tools for facilitating conversations in math class. It's also why we don't generally give students immediate feedback that their answers are "right" or "wrong." That kind of feedback often ends productive conversations before they begin.

But the classes that exist right now are hostile to the kinds of interactions we'd all like students to have with their teachers, with their classmates, and with math. Students are separated from one another by distance and time. Resources like attention, time, and technology are stretched. Mathematical conversations that were common in September are now impossible in May.

Our values are in conflict. It isn't clear to me how we'll resolve that conflict. Perhaps we'll decide the best feedback we can offer students is a computer telling them they're right or wrong, but I wanted to explore the alternatives first.

2020 May 25. The conversation continues at the Computation Layer Discourse Forum.

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When schools started closing months ago, we heard two loud requests from teachers in our community. They wanted: Written feedback for students. Co-teacher access to student data. Those sounded like unambiguously good ideas, whether schools were closed or not. Good pedagogy. Good technology. Good math. We made both.

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The standards for mathematical practices are the same for K-12 grade. Many times teachers need to know “How do I teach practice #1 at my grade level. The link above shows examples of the math…

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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Looking for mathematically rich problems to motivate, challenge, or inspire your students? The ODMP collection features intriguing, inquiry-oriented mathematics problems for grades 3-12, including topics in pre-algebra, algebra, geometry, trigonometry, and pre-calculus.

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Looking for mathematically rich problems to motivate, challenge, or inspire your students? The ODMP collection features intriguing, inquiry-oriented mathematics problems for grades 3-12, including topics in pre-algebra, algebra, geometry, trigonometry, and pre-calculus.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It’s an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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This activity will help students make the transition from one-variable representations (e.g., number lines) to the TWO-variable representation of the coordinate plane. Students will watch 15-second videos and translate them into graphs with your help. Special thanks to Adam Poetzel (@adampoetzel) for his videos. (Used under CC-BY license.)

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I train mathematics educators who want their students to be better problem solvers.

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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Website with Templates of all Kinds for Number Talks

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Website with Templates of all Kinds for Number Talks

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Access Google Sites with a personal Google account or Google Workspace account (for business use).

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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Website with Slides for Dot Talks and Ten Frames

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Website with Slides for Dot Talks and Ten Frames

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Math / Kindergarten Number Talk Resources

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New to Number Talks? Read the following article to find a summary of the Number Talks idea!(Content for slides below come from Number Talks by Sherry Parrish)Five and Ten FramesNumber 3(The slides above were compiled by Mary Elizabeth Mendenhall from Griffin RESA.)

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Understanding Language: Mathematics Instruction for ELs Article

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Understanding Language: Mathematics Instruction for ELs Article

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Searching the internet and more for the best apps and tech tools for a 1 iPad classroom

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don't go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don't go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day's mathematical practice, as "warm ups" for other lessons, or as stand-alone extended engagements with mathematical concepts. The teachers in these videos are from schools participating in the Silicon Valley Mathematics Initiative.

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Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day's mathematical practice, as "warm ups" for other lessons, or as stand-alone extended engagements with mathematical concepts.

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Open Middle - Challenging math problems worth solving

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Open Middle - Challenging math problems worth solving

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Open Middle - Challenging math problems worth solving

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Open Middle offers interactive math problems designed to foster critical thinking. Explore unique challenges that boost problem-solving skills and creativity.

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There's a lot happening in elementary mathematics and it's really tough for teachers to keep up with it all...let alone parents and administrators.

I keep reminding myself that the turtle won the race.

It's my hope that in creating and sharing this video, we can all slow down a little bit more and focus on building fluency through conceptual understanding.

Hope it helps!

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There's a lot happening in elementary mathematics and it's really tough for teachers to keep up with it all...let alone parents and administrators. I keep reminding myself that the turtle won the race. It's my hope that in creating and sharing this video, we can all slow down a little bit more and focus on building fluency through conceptual understanding.