Live from the Café Podcast: The Missing ‘M’ in STEM Education

By Marinell Rousmaniere

 

During the Social Impact Connect conference at Venture Café, I had the opportunity to moderate the conversation around the Missing ‘M’ in STEM Education. The discussion goes to the core of mathematics education and proficiency that drives achievement in Science, Technology, and Engineering careers. I was joined by a cross sectional panel that dove into the nuts and bolts of math teaching and learning through their years of experience and research. The panel included Julia Bott, Principal at the Ellis Mendell School in Boston Public Schools, Aparna Rayasam, Vice President of Engineering at Akamai Technologies, and Justin Reich, Assistant Professor & Director at MIT Teaching Systems Lab.

The following are a few highlights from the discussion, the full conversation is available here. Portions have been edited for clarity.

 

Marinell: Mathematics is often an overlooked aspect of STEM yet is instrumental to unlocking potential in S, T, E – Science, Technology, and Engineering careers. What gets lost when math is overlooked? Why do you think giving math education more attention is so important?

Aparna: This is a multi-dimensional problem that manifests in different ways. When I compare notes with peers in other industries, we are seeing that more and more things we do rely on machine learning, data science, AI, and other technological tools to assist with our solutions. When you scratch the surface and remove the buzzwords, all these things stand for advanced math. A phrase industries don’t use enough is “true math experts”. Twenty years ago, complex techniques including neural network and applying mathematical models was in the domain of academia and educational experts. Large enterprises like Google and Facebook have democratized these techniques, so they are widely available now; the difficulty is finding the correct application which requires a knowledge of mathematical theory. Enterprises like ours, who want to move faster, want individuals who have this mathematic foundation. There is a supply and pipeline problem for experts who can truly understand this data.

Julia: When you look the data, a third of students are proficient in Math by 8th grade within Boston, which reflects the national average. That has grave implications for the future success of our students. Through a college and career readiness lens, if students come in thinking of themselves as mathematicians, learners and thinkers, someone who gets the answer quickly in the elementary grades but begins to struggle as they move up grade levels as problems become more complex that has terrible implications for college and their future careers. Students who are already marginalized by race, social economic factors, and other barriers experience these implications at a higher magnitude.

“Having an adaptive teacher with skills, knowledge and pedagogy and even thinking that math is not about getting the right problem but about productive struggle with problem solving and perseverance is groundbreaking”

Justin: An alternative to the student who is ‘good’ at math – as someone who gets the right answer quickly – is the student who sticks with it or struggles and perseveres. Studying math learning across the world, this is the case in other countries. Being ‘good’ at math is being at the board and struggling with something and not getting the answer quickly. These issues as Julia points out are identity issues, how do you get students to feel good about themselves as they persist when with struggling against these puzzles?

Math is central and a gatekeeper to all other STEM activities. In the absence of a fundamental understand of Algebra I, it’s hard to comprehend biology, chemistry, physics, computer science, and all these other STEM-related areas.

Aparna: That’s a great point. Productive struggle in the industry is lacking as well. You have to respect the problem. If the problem was solvable in a couple of days, we wouldn’t need the individual to think through it. We need to cherish patience and perseverance.

Marinell: Math proves to be one of the strongest indicators of long-term success. Getting those foundations early in school matters a lot as you move up through concepts and formulas to more advanced courses. When you look deeper in the data, math achievement becomes a significant indicator of future earnings.

Julia, as an educator and school leader, why has moving the needle on this issue has been so hard? What has been participating challenging with teaching and learning in math?

Julia: The problem has never been and never will be the children. All children are intellectuals. They all come to school as sense makers, as problem solvers, as thinkers. They have natural abilities to figure things out.

The really hard question then becomes whose problem is it? At schools, we have to look at ourselves in the mirror and ask hard questions about our beliefs in students in front of us, our own content knowledge, mathematical thinking, productive struggle, and perseverance; what is a worthy task and what does it look like to put one in front of children to create this space for them to showcase their ability to make sense and grapple with problems?

What does it look like to train teachers? It was always procedure, procedure, procedure. You had to memorize things. When the upper grades required conceptual learning about numbers, kids fell apart as their mathematical thinking had to be more flexible and the gaps become wider and wider. It became clear we needed support to think differently about how we approach the content and structure of learning so kids can build the skills and competencies to be successful.

“Math is central and a gatekeeper to all other STEM activities”

Justin: As Julia mentioned, teachers doing more math thinking themselves will help them teach it to their students. Moreover, some form of discreetly individualized coaching is proven to help math teaching. One of our observations is that when teachers learn, they have insufficient opportunities to practice that learning. Teachers listen and talk with each other about teaching but very rarely are they able to practice. A stark contrast to other ‘helping’ careers, like social workers – they practice on each other and talk about it practically. Teachers have less of that opportunity.

Our team is always wrestling with innovative approaches to these problems and right now we are wrestling with ways to create practice spaces for teachers to rehearse and reflect on important decisions for teaching. In the fall, we’ve been working with 20 third grade math teachers on a tool we call Eliciting Learner Knowledge, a paired synchronous chat-based game where one individual is given the role of a teacher and the other is the student. A transcript is generated from all these chats and we are able to reflect upon strategies we use to better communicate with students. In the spring, we will be working on “Teacher Moments”, a digital simulation tool meant for individual play on a handheld device that immerses you with vignettes of classroom life.

Marinell: Thank you so much for all of your thoughts, it echoes the way we think of leveling the playing field in math achievement. Our leverage point is largely with teachers – the individuals that have the most impact on student outcomes. Having an adaptive teacher with skills, knowledge and pedagogy and even thinking that math is not about getting the right problem but about productive struggle with problem solving and perseverance is groundbreaking. To be able to bring this kind of thinking to teachers and have them teach math in a different way for their students is a scalable action and advocacy plan to reduce skills and knowledge gaps.

 

The entire conversation is available here.

 

Marinell Rousmaniere is the President & CEO of EdVestors.

My path to college included an arts internship that infused my life with creativity — and a clerical skill set, too

The October 24, 2019 Hechinger Report Student Voice op-ed by Eleasah Whittaker, “My path to college included an arts internship that infused my life with creativity — and a clerical skill set, too”, details Eleasah’s experience with Actors’ Shakespeare Project through the inaugural Boston Bloomberg Arts Internship in Summer of 2019 and the benefits of having access to real world experiences. From the article:

While I had 11 years of music experience under my belt, I had no experience with sound design, and the show was set to open only two-and-a-half weeks after my first day! That was nerve-wracking, to say the least. I had come into the project with the idea that I would be composing music for the show, but I quickly realized that this goal was unwise given the time constraints. Instead, I composed small themes for the different scenes, and then supplemented those themes with sound effects. Since the program’s participants were putting on a production of Shakespeare’s The Tempest, the sounds included crashing waves, beach noises and spooky magic.

Read the full article here and learn more about the Bloomberg Arts Internship program here.

National Arts in Education Week celebrates the transformative powers of creative skills

The September 9, 2019 Hechinger Report Op-Ed article by Marinell Rousmaniere and Myran Parker-Brass, “National Arts in Education Week celebrates the transformative powers of creative skills”, describes the impact of arts education and its ability to equip young people with necessary skills to exceed in school, work, and life. September 8-14, 2019 is National Arts in Education Week. From the article:

Arts education for all students is fundamental to a well-rounded education. The arts provide dimension and perspective, and they help students develop the critical thinking, communication and collaboration skills they will need to succeed in school, work and life. Students who have high-quality arts learning opportunities may be among tomorrow’s great artists, and they also may be among tomorrow’s health care professionals, engineers and civic leaders. No matter the path, arts education provides a way to creative careers of the future.

EdVestors and Boston Public Schools (BPS) began laying the groundwork for this future more than a decade ago with the creation of BPS Arts Expansion, an initiative that has brought arts learning opportunities to 17,000 additional students annually across the entire school district, ensuring all students receive foundational arts learning opportunities. Now, it’s time to build upon this base and increase opportunities to help students put their arts education into action.

Click here to read the full article.

Mayor Walsh, Boston Public Schools and EdVestors Announce Over $350,000 in Arts Expansion Grants at Annual Citywide Arts Festival

    

 

As the BPS Arts Expansion initiative marks its 10th anniversary, the new grants to nearly 60 schools highlight an ongoing commitment to expand quality arts education across Boston

 

BOSTON (June 4, 2019) – Boston Public School students will continue to receive their quality arts education programs throughout the 2019-2020 school year with today’s announcement of more than $350,000 in grants that will support nearly 60 schools working with more than 30 arts partners across the city. The annual grants are part of the successful Boston Public Schools (BPS) Arts Expansion initiative, which is celebrating its 10th year in bringing quality arts instruction to underserved neighborhoods.

The City of Boston, BPS and EdVestors announced this latest round of funding during the seventh annual BPS Citywide Arts Festival, a three-day celebration on the Boston Common featuring more than 1,100 BPS student performers and exhibitors.

“We are grateful to our partners in Boston Public Schools Arts Expansion who have worked tirelessly for 10 years to bring equity and access to arts education to our schools and inspiration to our students, many of whom are showcasing their talents at the festival today,” said Mayor Martin J. Walsh. “We are also celebrating the third year of our Boston Creates plan to make arts and culture as fundamental to the City of Boston’s identity as its history and traditions. Our goal is to make Boston residents, young and old, feel welcome to engage in the city’s thriving arts scene. I hope many of us are encouraged, as I am year after year, by our students who have embraced their own creativity and are willing to share it with us.”  

The BPS Arts Expansion initiative is a multi-year effort focused on increasing access, equity and quality of arts learning for all BPS students. The 2019-2020 school year grants will mark the 11th year of grant-making for the Arts Expansion Fund and the second year for Phase 4 of the initiative and the Fund (2018-2021). As part of this fourth phase of the BPS Arts Expansion initiative, the Walsh Administration and BPS, in collaboration with EdVestors, are working together to raise $3 million to sustain high levels of arts education in the district over a three-year period. 

As a result of this ongoing collaboration, there are now 80 percent more arts teachers working with 65 community arts partners providing arts instruction to 17,000 more students each year as compared to a decade ago. From 2009-2019, the percentage of BPS pre-K-8th grade students receiving a minimum of weekly, year-long arts instruction or its equivalent increased from 67 percent to 97 percent.

“For the past decade, Boston has led the nation in reinvesting in arts education by generating and sustaining a collective effort among the public, private and philanthropic sectors that has been bucking the national trend of declining arts opportunities in schools,” said Marinell Rousmaniere, President & CEO of EdVestors. “Supporting our children’s creative and intellectual growth through the arts is an important investment in our future. We have come this far due to our partnership with the Boston Public Schools and our dedicated partners who invest in closing this opportunity gap too many students experience.”

To date, donors including the Barr Foundation, the Boston Foundation, The Klarman Family Foundation and Linde Family Foundation have committed funds to ensure all preK-8 students receive weekly year-long arts instruction and that 100 percent of BPS high school graduates meet the Massachusetts Core Curriculum graduation requirement of one year of arts instruction. Notably, there has been a significant 5:1 return of increased public investment for every private dollar invested through BPS Arts Expansion.

“For 10 years, the BPS Arts Expansion initiative has successfully brought together classroom arts teachers, school leaders, teaching artists from our nonprofit partners, families, higher education and cultural partners, and funders,” said BPS Interim Superintendent Laura Perille. “Arts education has a remarkable impact on students’ academic, social and emotional outcomes. The arts make learning more engaging, and open up our students’ minds in ways that will help them become successful in college, career and life.”

The decade-long impact of the Arts Expansion can be seen on display throughout the week at the annual BPS Citywide Arts Festival, as student performers and exhibitors from schools celebrate the power of creativity, joined by parents and community members. The Festival, which runs June 4 through June 6 on the Boston Common, features students ranging from kindergarten through eighth grade, presenting visual arts exhibits and vocal, musical, dance & theatre performances.

“As a BPS Theatre Arts teacher for the past 16 years, nothing has made a bigger difference in my ability to effectively reach student actors, designers and audiences than the support through BPS Arts Expansion,” said Emily Culver, at the Thomas Edison K-8 School in Brighton. “During my first several years of teaching I was by myself, with no budget whatsoever, doing productions in a school with no materials for sets, costumes, props or lighting equipment. Over the years of receiving grants through the Arts Expansion, our school has had incredible privilege of partnering with professional Scenic Designers. This has allowed the Theatre experience to become tangible and authentic for everyone in the school, and has encouraged the community to attend our performances as well. Without a doubt it has elevated the rigor of the program and continues to be a critical component of our ability to provide a well-rounded, integrative arts education at the Edison K-8 School.”

More information on the BPS Arts Expansion is available here.

By Teachers For Teachers: What made teachers’ practice change?

This blog post is the third in a series of blogs written by a group of teachers who designed and led a five-session course for Boston math teachers. Please check out part one and part two of this series.

By Heidi Fessenden (District Elementary Math Coach, Cambridge Public Schools), Maggie Roth (Second grade teacher, Match Community Day Public Charter School), and Michelle Sirois (Fourth grade teacher, Perry Elementary School)

What made teachers’ practice change?

We were curious to find out more about which parts of our teacher-led math course, Bridging Classrooms, had led to such deep changes in teachers’ practice. To find out more, we interviewed some of the course participants in pairs. A few themes emerged as to why this professional development had such an impact on their teaching.

Safety for Adults, Safety for Kids

A few teachers, particularly early-career teachers, spoke about how safe they felt in this group. “I could take my shoes off there, literally and figuratively,” Shona Daye, a 4th grade teacher at the King School, said. The first day, she said, she was worried that she wouldn’t solve the math task correctly. “I was looking around, trying to see if I was using the ‘right’ strategy,” she recalled. She soon realized that getting the “right” answer or using the correct strategy was not the focus of the course. Instead, the focus was on the many ways we can arrive at solutions and on the depth and variety of thinking in the group.

“…After we shared out, you know, that fear just dissipated, and looking at different perspectives, I had all these epiphanies. And I wanted my students to feel the same way.”

Shona realized that if this safe environment to explore thinking made her feel safer, it would do the same for her students. “Allowing the children to explore and not give right answers, but just explore — That is phenomenal, that is huge, and totally engages everybody. Everybody was willing to take a risk. Nobody had a right or wrong answer. And that was exciting. That was really exciting.”

Experiencing Math as Learners

Shona and Emily Kmetz, a Tech Boston math teacher, both talked about how important it was to acknowledge they struggled with the same math problems they gave to their students. “My students loved hearing that I had trouble with the same problem they were solving,” Emily said. It also provided insights into how it feels to take on a challenging problem, learn and understand someone else’s strategy, and a window into the different strategies their students might use.

Teachers had experiences of being stuck, of struggling to collaborate with a partner, of feeling frustrated because someone else solved the problem faster than they did — all of which helped them remember the challenges of being a math student.

Teacher-led

In written reflections and interviews, many of the participants in the course mentioned that their curiosity was piqued by the idea of teacher-led PD. “These are teachers who are in the classroom every day, like me,” Retha Reynolds, a 5th grade teacher at the Sumner, said. “They know.”

When teachers had questions about the reality of implementing something in the classroom, or a challenge they face daily, the facilitators had ideas because they face the same challenges. Teachers experienced the course as more practical and useful than a class led by an “expert” who is not a teacher.

Expertise in supporting students with special needs to talk, struggle, and achieve more

Several participating teachers work primarily with students with special needs. They expressed frustration with the number of professional development sessions they have attended that don’t speak to the specific needs of their students. Although this course was not billed as a course directed toward special educators, the facilitators were all teachers who often teach students with special needs. The focus on making math a more visual, creative, and discussion-oriented subject appealed to the special educators in the group. They enthusiastically tried out new instructional routines and protocols they learned in Bridging Classrooms, such as number talk images (see image, right).

Retha enthusiastically adopted Three Act Tasks as her pedagogy of choice after doing the Toothpick Task in class. (Read a summary of the structure of a Three Act Task here, and see how Dan Meyer breaks one down here.) After our course was over, she reflected on how well the visual and storytelling aspects of many of the tasks she did in our course worked for her students.

When she started to use Three Act Tasks and have her students notice and wonder, she noted that, “The kids [were] answering the questions and talking to each other about what they saw happening in the picture before I could even present what the problem was.”

For Retha, getting her students talking about a visual or a story was the key to both increasing conversation and engagement, and strengthening her students’ ability to persevere and struggle.

“I felt like before I was kind of guiding them too much. I was doing too much for them…. I began getting them to really talk about the math [first] which gets them to thinkabout what it is they’re doing. I felt like I was able to just step back and let them struggle with it.”

With these reflections, we are continuing to share our learning with partners and leaders in the math community. Recently, Heidi and Michelle fpresented to leaders in math education at the National Council of Supervisors of Mathematics (NCSM) conference in San Diego. In doing so, they asked participants – and we ask you – “What allows teachers and students to feel safe taking risks doing math in your setting?” and “How can you increase opportunities for teachers to feel safe and take risks as learners?”

 

Melissa Frascella (Math Dept Chair / Eighth grade math teacher, Boston Collegiate Charter School), Meredith Hart (Sixth grade teacher, Haley Pilot School), and Alia Verner (Math Director / Instructional Coach, TechBoston Academy) also contributed to this blog post.

To learn more about Zeroing in on Math, click here.

Part One – By Teachers for Teachers: Learning and Growing as Math Educators

Part Two – By Teachers For Teachers: Changing the Culture of Math Class

EdVestors to Receive $100,000 Grant from the National Endowment for the Arts

   

 

 Funding will support the collective work of expanding arts education in Boston

 

(BOSTON) May 15, 2019 – National Endowment for the Arts Acting Chairman Mary Anne Carter has approved more than $80 million in grants as part of the Arts Endowment’s second major funding announcement for fiscal year 2019. Included in this announcement is an Art Works grant of $100,000 to EdVestors for Phase 4 of Boston Public Schools Arts Expansion (BPS-AE), a multi-year collective impact effort serving 54,000 students across 125 Boston Public Schools. Art Works is the Arts Endowment’s principal grantmaking program. The agency received 1,592 Art Works applications for this round of grantmaking, and will award 977 grants in this category.

 

“These awards, reaching every corner of the United States, are a testament to the artistic richness and diversity in our country,” said Mary Anne Carter, acting chairman of the National Endowment for the Arts. “Organizations such as Edvestors are giving people in their community the opportunity to learn, create, and be inspired.”

 

As the backbone organization of BPS-AE since 2009, EdVestors will continue its successful approach collaborating with BPS to increase the capacity of schools and the central office to support high quality arts instruction; using incentive-based grantmaking to increase and deepen arts experiences for students; coordinating effective partnerships; and engaging stakeholders to build broad ownership and ensure long-term sustainability of arts education in Boston.

 

“We are grateful that the NEA recognizes the power of collective impact to advance arts learning opportunities across this country,” said Marinell Rousmaniere, CEO of EdVestors. “As we mark the tenth year of Boston Public Schools Arts Expansion, this additional support reinforces our strong commitment to increasing equitable access to quality arts education for students across Boston.”

For more information on this National Endowment for the Arts grant announcement, visit arts.gov/news.

 

About EdVestors

EdVestors’ mission is to increase the number of schools in Boston delivering dramatically improved educational outcomes for all students. EdVestors is a school improvement organization that combines strategic philanthropy, education expertise, and implementation support to help schools create the conditions for school change. EdVestors seeds promising ideas through the School Solutions Seed Fund, shines a spotlight on school improvement through the School on the Move Prize, and scales efforts to close opportunity and achievement gaps through three strategic initiatives: Boston Public Schools Arts Expansion, Zeroing in on Math and our newest effort to expand Career and Technical Education pathways. Learn more at www.EdVestors.org.

###

An office that promotes deep thinking

The April 3, 2019 Boston Globe article by James Vaznis, “An office that promotes deep thinking”, showcases the EdVestors’ office space reflecting the work being down across program areas to expand arts education, math rigor, and career pathway opportunities for Boston’s public school students. From the article:

For decades, women across Boston would come to the YWCA building in the Back Bay to swim laps in a pool on the fourth floor to stay healthy and vibrant. Now, that historic space is being used for the offices of the education nonprofit EdVestors, which is helping to transform public schools in Boston.

Read the full article here.

April 9th: EdVestors 17th Education Showcase

Find out what the hottest issues in urban education are at this year’s Showcase, which will feature extended time to directly engage with teachers, school leaders and non-profit partners, who are tackling the most pressing challenges in Boston’s schools through EdVestors’ Seed Fund. In addition to learning about a range of key urban education issues and schools’ innovative and practical solutions, guests will have the opportunity to deepen their knowledge of the immigrant experience in Boston schools or explore how schools are honoring race and identity in the classroom. We are also excited to highlight a conversation on re-imagining high school education  with Jal Mehta, PhD, Associate Professor at the Harvard Graduate School of Education and author of soon-to-be-released In Search of Deeper Learning.

 

Click here to RSVP.

Inspiring Students One Coffee Cup at a Time – East Boston High School’s Hospitality and Tourism Partnership with Starbucks

By Eliza Cassella 

In an era of innovative learning, East Boston High School is focused on leading the way by creating unique opportunities for students to engage in authentic learning experiences through its Career & Technical Education (CTE) Pathways. East Boston High School offers a pathway option for every student to participate in during their junior and senior year. These pathway programs expose students to a wide array of post-secondary career opportunities, all with a goal of presenting students with extensive immersive experiences in a field that could lead to potential careers while equipping them with the necessary skills to be successful. This year, East Boston High School has taken a strategic approach to leveraging industry partners by providing job shadows, leadership development, and site visits in the field to provide an experiential work-based learning experience for students to apply what they are learning in the classroom directly to the field.

Recently, students enrolled in East Boston High School’s Hospitality and Tourism Pathway, led by their teacher–Mr. Joe Bruno, participated in a full day of leadership development with our newest partner–Starbucks. After several weeks of planning, students traveled to the Starbucks Lynn location for their immersive workplace visit. Upon arrival, students were quickly welcomed with a coffee tasting- a component of Starbucks culture that starts every company meeting, gathering, or event. The coffee tasting quickly set the tone for a day that would be enriching for students and connected to the company’s mission and values.

Following the coffee tasting, students rotated through different stations where they reflected on their individual strengths, discussed the importance of giving and receiving feedback, and how to identify a workplace that connects to one’s own personal values. Each of these stations explored different components of the Starbucks onboarding process for employees, allowing our students to learn about both the hard and soft skills required to be a successful employee. Students reflected on the skills which included: organization, communication, dependability, empathy, problem solving, optimism, and warmth– all essential to be a successful Starbucks employee. The visit concluded with a testimonial from an East Boston High School alum, who was recently named Store Manager of the Year, and the opportunity to apply and be interviewed at any Starbucks in the greater Boston area.

“I learned that I’m a leader even if sometimes it’s hard for me to recognize it and view it as for what it is. I learned that we all have a different story to tell.”
– Delmy, East Boston High School senior

Through the discussions, students were also able to make connections to experiences from other industry visits and identify themes around the overall skills necessary to be employable and prepared in the Hospitality and Tourism industry. These connections were shared in a debrief at the end of the day where it became evident that students were demonstrating a deeper sense of confidence in sharing their own stories and work experiences. Students shared how hearing directly from hiring managers reaffirmed many of the lessons they learned in the classroom and how valuable the innate qualities and skills they bring to the workplace truly are. One student explained how she never realized the value of speaking two languages, and how marketable of a skill that is on her resume when applying for a job.

The Starbucks mission states, “to inspire and nurture the human spirit- one person, one cup, and one neighborhood at a time.” Through this partnership, students will continue to gain invaluable real-world learning experiences, gain employment opportunities, and can work towards a college degree paid by Starbucks—one student, one cup, one community at a time.

Pictured with his class is Mr. Joe Bruno, East Boston High School Hospitality and Tourism Pathway Teacher

Eliza Cassella is the Director of Partnerships & CTE Pathways at East Boston High School.

To learn more about East Boston High School’s CTE Pathways, click here

For more information about EdVestors’ CTE work, click here.

A math classroom full of “sweaty brains”

By Michelle Sirois

A classroom teacher currently engaged in Zeroing in on Math’s Deeper Learning work and former EdVestors’ Math Fellow.

Over the past few weeks, my fourth-grade math class at the Oliver Hazard Perry Elementary School worked together on multiplication. We tackled word problems that challenge students to connect relevant components of questions, apply mathematical thinking and knowledge to their approach, and prove their answers through alternative solutions. The curriculum recommends a lesson plan that first presents a problem to the students, then allows the students to solve the problem, and finally provides more problems for students to work on.

We often tell students to take risks and make mistakes because they lead to learning. Yesterday, my own mistake led to lots of learning, excitement, challenges, and opportunities for more learning.

We recently encountered our first word problem that involved division and I decided to slightly alter the introduction of the problem. I did this by removing the questions, to see what students would notice and wonder about the problem. However, in doing so, I accidentally removed the total numbers of apples too.

The question read:

Mrs. Santos owns a neighborhood grocery store. She has some apples to arrange in rows for her window display. She has room for 4 rows in her window.

(The scenario I meant to give them read that Mrs. Santos had 52 apples to arrange in 4 rows.)

Productive curiosity

Upon hearing the lively chatter around the room, I decided not to share the original problem with the total number of apples.  I challenged my fourth graders to think about how many apples there might be in total and how they might go about representing the situation. In our classroom, we have a range of math proficiency from one student working at a first-grade level to students far above grade-level. Students played with various approaches to a solution: some worked with cubes, some tried factors of 16, others pushed themselves to multiply with larger and larger numbers they haven’t multiplied before!

We reconvened as a class after fifteen minutes to discuss what different groups tried. I began the conversation with the notion that many groups wrestled with: that Mrs. Santos only had 16 apples. Half of the class was convinced 2 rows of 8 apples was possible until their classmates pointed out the problem stated she had 4 rows to work with. Group after group presented their work around multiplication until one student came to the revolution that “this is a division problem!” He explained his reasoning and I saw light bulbs go off in their heads and hands shot up with excitement!

One group who placed 98 apples on each row shared their work and found 98 x 4 = 392. Their classmates were intrigued by the large numbers and mentioned how large the windows must be to fit all the apples,

I promised the class more time to work on the problem after lunch and cheers erupted across the classroom, “My head is exploding with ideas!” One student who often confuses mathematical concepts whispered, “This is the best math class ever – it’s starting to make sense now!”

 “Sweaty Brains”

At the Perry, we celebrate “sweaty brains”. A sweaty brain happens when students challenge themselves with harder problems than what is asked of them. Exercising their brains furthers their conceptual knowledge.

After lunch, I wrote out key questions: How many apples are in each row? How many apples does Mrs. Santos have in all? Where does this concept show up in their work? Where does this show up when writing both the multiplication and division equations of this situation?

Students challenged themselves with more and more 3-digit numbers and checked in with me to see if they were right. I asked them to prove their work by using another strategy, so they kept multiplying and dividing with more and more large numbers!

Engaged and joyful learning

When it was time to wrap up, the students groaned and wished they had more time – I was ecstatic to hear it!  Before leaving class, each student had to solve the original problem that stated Mrs. Santos had 52 apples to arrange equally in 4 rows. I was impressed that all but 5 students correctly solved the problem using multiplication and division concepts they learned and retained. For the 5 students who didn’t solve the problem correctly, I now have a targeted approach to talk through their misconceptions.

As any teacher will tell you, teaching can be mentally, emotionally, and physically. But yesterday, it was just pure joy. Every kid stayed engaged with one problem for over an hour – one problem! This lesson reminded me that kids don’t need to do ten, twenty, or hundreds of problems to learn. They just need the right context and questions to explore – and with that, learning is engaging, invigorating, and joy-filled.

 

To learn more about Zeroing in on Math, click here.

The Oliver Hazard Perry K-8 School was a 2018 School on the Move Finalist, click below to learn more about the Perry K-8.