Marshall Memo 821

In This Issue:

Quotes of the Week

“You’re not always gonna win in life, you’re not always gonna be number one, you’re not always gonna be the top, the best, and get everything. So, when you lose, you got to learn how to take that losing and know what to do with it.”

A Chicago high-school student on what she learned on the debate team (see item #2)

“In a 2019 survey by the Pew Research Center, black respondents were more likely than any other racial group to report that they felt people were suspicious of them (65 percent), that people acted as though they were not smart (60 percent), that they were treated unfairly in hiring, pay, or promotion (49 percent), and that they had been unfairly stopped by the police (44 percent).”

Karyn Lacy in “How to Prove You’re Middle Class” in The New York Times, January

22, 2020, https://nyti.ms/2O50PHH

“Without knowledge, learners struggle at every stage of the reading process, from decoding to fluency to making higher level inferences.”

Sara Lupo, Alicia Berry, Emma Thacker, Amanda Sawyer, & Joi Merritt (see item #7)

“Can you imagine going to a job where you learn all about the different types of buttons, threads, fabrics, and zippers but no one tells you that you are manufacturing jeans? Yet that’s often how reading instruction can feel for children.”

Heidi Anne Mesmer (see item #5)

“When we start to break down the barriers between ‘school day’ and ‘afterschool,’ we are taking a giant step toward being a full service to our students and families.”

Eva Jo Meyers (see item #4)

1. Reducing Burnout and Attrition Among Special Education Teachers

In this article in Exceptional Children, Elizabeth Bettini (Boston University) and six colleagues say that teachers working in self-contained settings with students with emotional and behavioral challenges have a higher rate of burnout and attrition than other educators. This is a serious problem because it means the most vulnerable students, who have the greatest need for effective instruction, lack instructional continuity and are often working with novice teachers – all of which puts those students at greater risk of poor long-term outcomes.

Bettini and her colleagues surveyed a national sample of special educators on the following workplace factors:

– Administrative support (help with classroom management, behavior plans, coaching);

– Curriculum resources (scope and sequence, materials, books);

– Collaborative culture (teachers’ input was valued, colleagues were helpful);

– Collective responsibility (a role in schoolwide discipline and instruction);

– Planning time (opportunities to prepare lessons and work with other teachers);

– Paraprofessional training (their skill with discipline and instruction);

– Paraprofessional trust (the teacher could count on support personnel);

– Instructional grouping (a manageable mix of skill and behavioral needs);

– Workload manageability (enough time within school hours to do the job well);

– Stress (dealing with inappropriate behavior and verbal and physical aggression);

– Emotional exhaustion (feeling tired, emotionally drained, and burned out);

– Intent to stay (not thinking about shifting to another clientele, school, or profession).

The researchers looked at how these factors interacted in schools and found that demands, resources, and affective responses accounted for 58 percent of variance in teachers’ intent to stay. Some specific findings:

• Teachers’ sense of a manageable workload was most influenced by three things: demands (especially class composition), time to plan, and curriculum resources. When resources were low and demands were high, teachers were most likely to burn out and want to leave. One of the most negative factors in terms of teachers’ stress and emotional exhaustion was having to supervise more paraprofessionals. Having heterogeneous classes with a challenging mix of achievement and behavioral demands also contributed to burnout. Surprisingly, teachers’ perceptions of a school’s collaborative culture and sense of collective responsibility were not strong predictors of burnout and attrition.

• Emotional exhaustion was the link between workload manageability and intent to leave. “Burnout is similar in symptomatology to depression,” say Bettini et al., “so it is understandable that emotionally exhausted teachers would seek another job.” Surprisingly, stress was not strongly correlated with desire to leave, perhaps because challenging student behaviors often motivate teachers to seek out effective interventions.

• Administrative support directly and indirectly predicted the likelihood that teachers would stay. The researchers believe this was because supportive administrators were taking care of a number of factors: planning time, curriculum resources, scheduling, class composition, paraprofessional assignments and training, and school culture.

• There was an interesting interaction among instructional grouping, curriculum resources, and planning time. The researchers believe this might be because teachers with more-manageable homogeneous groups had less need for differentiated materials and planning (or after-hours) time to create additional materials for students’ varying needs.

The bottom line: when special educators in self-contained settings say they are overwhelmed, “leaders should take those concerns seriously,” say Bettini and her colleagues. “We encourage leaders to ask why they feel overwhelmed and find ways to reduce demands or increase resources, with a focus on protecting planning time and supporting paraprofessional supervision.”

“Predicting Special Educators’ Intent to Continue Teaching Students with Emotional or Behavioral Disorders in Self-Contained Settings” by Elizabeth Bettini, Michelle Cumming, Kristen Merrill O’Brien, Nelson Brunsting, Maalavika Rugunathan, Rachel Sutton, and Akash Chopra in Exceptional Children, January 2020 (Vol. 86, #2, pp. 209-228), available for purchase at https://bit.ly/2O4c2Is; Bettini can be reached at lbettini@bu.edu.

2. High-School Debate and “Cultural Capital”

In this American Journal of Education article, Karlyn Gorski (University of Chicago) reports on her six-month study of two urban high-school teams taking part in the interscholastic Chicago Debate League. Observing their practice sessions and competitions and interviewing students and their coaches, Gorski concluded that debate allowed students to acquire three forms of cultural capital: being confident asking for and using critical feedback; deconstructing and analyzing complex ideas; and building on their already existing ability to face failure with resilience, and persevere. These attributes equipped debaters to compete more successfully on what Gorski describes as the profoundly uneven playing field of U.S. secondary schools.

Gorski says that students from all backgrounds enter classrooms with cultural capital, but certain kinds are more valued than others by dominant institutions like schools – which gives an advantage to more-privileged students. For example, sociologists have found that most middle-class children feel empowered to demand customized interactions with authorities like teachers and doctors; poor and working-class children, on the other hand, learn to display a “sense of constraint” marked by compliance with rules and practices. Similarly, middle-class kids learn to navigate problems at school using “strategies of influence,” while working-class students are taught to use “strategies of deference.” In college, more-entitled students are comfortable interacting with instructors, while students from high-poverty schools often exhibit discomfort, which doubly disadvantages them.

Gorski provides further commentary on the three forms of cultural capital she observed students developing on the debate teams:

• Using feedback – “Debaters learned, through repeated interactions with peers and authorities in the debate space, to request high-quality feedback that they could use to their own advantage,” says Gorski. “Feedback was seen as crucially important to improving one’s debate skills, and strategies for responding to it were seen as valuable beyond the debate setting… When feedback was given, it was rarely accepted as adequate. ‘Anything else?’ was a constant refrain from debaters after receiving criticism… Comfort placing demands on figures of authority, such as requests for assistance, accommodations, and attention, is a form of dominant cultural capital that is highly valued in educational settings.”

• Evaluating complex ideas – Debate preparation constantly exposed students to challenging arguments and ideas. Competing, along with being asked to take both sides of an argument, sharpened students’ analytic skills. In the process, says Gorski, debaters acquired “habits of mind” and “sophisticated skills of interpretation and analysis” that they had not learned at home or in classrooms. “Familiarity with complex literatures, as well as the strategies debaters use to understand them, set these students up for success in challenging courses throughout high school and college.”

• Resilience – Being able to bounce back from a specific failure is especially important for disadvantaged youth, says Gorski; she calls this “adaptive cultural capital” and adds that it’s especially important for disadvantaged students. Debate is uniquely suited to fostering this ability since debaters are constantly told that losing is a valuable experience. Gorski quotes one student: “You’re not always gonna win in life, you’re not always gonna be number one, you’re not always gonna be the top, the best, and get everything. So, when you lose, you got to learn how to take that losing and know what to do with it.” Many debaters regarded learning, rather than winning, as the goal, and developed specific strategies for dealing with – and learning from – defeats.

Is it possible, asks Gorski, that students who go out for debate already have these three cultural attributes? It’s true that competitive debaters enter high school with higher eighth-grade test scores than nondebaters, and there is some self-selection with students who choose an academically challenging extracurricular. “However,” says Gorski, “it is important to note that even if all of the debaters are driven, motivated, prosocial, and academically excellent students, the key finding presented here still holds: it is possible for certain doubly disadvantaged students to gain dominant and adaptive cultural capital within their under-resourced neighborhood schools… They built these skills over time and spoke often of the differences between their confidence and capabilities before and after joining the debate team. In their own perspectives, debate was a crucial factor in their ongoing development.” One girl spoke of her “debate brain… that’s where my whole mind turns on; it like, sucks everything up.” This student said her “debate brain” turned on only in tournaments, not at school, where regular classes didn’t provide enough intellectual stimulation and actionable feedback.

“‘My Voice Matters’: High-School Debaters’ Acquisition of Dominant Adaptive Cultural Capital” by Karlyn Gorski in American Journal of Education, February 2020 (Vol. 126, #2, pp. 293-321), available for purchase at https://bit.ly/3aM3O1j; Gorski can be reached at

gorski@uchicago.edu.

3. Teaching The Odyssey with a Social Justice Perspective

In this Journal of Adolescent and Adult Literacy article, Jacob Steiss (University of California/Irvine) notes thatThe Odyssey is widely taught in U.S. high schools. Odysseus’s adventure-filled journey to reclaim his position as ruler and patriarch of Ithaca after a 20-year absence has a well-established place in the literary canon. Among the questions students are asked to consider:

– What makes this hero heroic?

– What can The Odyssey tell us about self-control and resisting temptation?

– How can we use close reading to affirm that this classic is a classic?

Steiss suggests having students read The Odyssey with a more critical eye, recognizing that all stories “are constructed and embedded with hidden ideologies.”

He himself took this approach teaching the epic to ninth graders at a private boys’ high school in New England. His goal was for students to imagine alternative viewpoints, and his lessons often followed this sequence: focusing on one passage (for example, Penelope expressing sadness and longing for her husband during his long absence); reading the passage closely; posing critical questions (for example, What does the text say is normal or desirable? What virtues can women have?); analyzing and discussing the text in small groups and as a class (often using Google Docs, monitored by Steiss); and then independently writing responses.

As students delved into the text with this critical perspective, they confronted questions like these:

– In what ways might our veneration of Odysseus condone infidelity, permit violence against women, and uphold a patriarchal social order?

– How does the text work to uphold the privilege of the elite despite social inequalities secured by lying, violence, and theft?

– How does this narrative, which validates male sexual conquest and villainizes female sexuality, reflect male sexual privilege and victim-blaming present in our society?

His goal, says Steiss, was for students to “engage in sustained critiques of the dominant narratives that they will encounter as critically literate citizens.”

In final essays summarizing what they learned in the unit, students wrote about entitlement and privilege, infidelity, double standards, women’s roles, violence against women, and the privilege of the elite. One student had this to say: “The privilege of the male perspective is often an unquestioned and unanalyzed element of texts, and if we don’t analyze this problematic construct we allow this representation to be accepted as a fact in our society.”

Given its troubling content, why not kick The Odyssey out of the canon? Steiss believes the epic has a place in the curriculum because it offers “opportunities for students to engage with issues of race, class, and gender and consider their responsibility to respond to social injustice.”

“Dismantling Winning Stories: Lessons from Applying Critical Literature Pedagogy to The Odyssey” by Jacob Steiss in Journal of Adolescent and Adult Literacy, January/February 2020 (Vol. 63, #4, pp. 433-441), available for purchase at https://bit.ly/2tKGGzV; Steiss can be reached at jsteiss@uci.edu.

4. Linking Afterschool Programs to the Regular School Day

In this Cult of Pedagogy article, Eva Jo Meyers remembers her experience with afterschool programs when she was a teacher: not knowing the names of teachers who took over after she left for the day; the annoyance of having to vacate her classroom right after dismissal; and being upset when her room was messed up by afterschool students. Then she became an afterschool teacher herself and developed a whole new perspective: “My frustration at being unable to connect with teachers in my afterschool role was only paralleled by my embarrassment at how oblivious I had been when I was a teacher.” Here are her suggestions for connecting the regular school day with afterschool programs:

• Exchange observations. Regular teachers should see afterschool activities and afterschool teachers should visit the day program, perhaps spending a morning in a classroom or leading an end-of-day debrief on what happened that day. It’s especially important for school-day teachers to attend special events and performances in the afterschool program. The key is to coordinate behavior systems, classroom expectations, and ways of supporting certain students, with both sides contributing ideas.

• Include afterschool staff in teacher events, grade-level meetings, and celebrations. This might include PD sessions, teacher team meetings discussing curriculum and students, and holiday parties.

• Invite afterschool staff to contribute feedback for, and participate in, parent-teacher conferences. “Afterschool staff see another side of students,” says Meyers, “a side that isn’t always visible during the school day.”

• Provide the teachers’ manual or answer key for homework, and offer tips on how best to help students with your assignments. This makes all the difference for afterschool staff when they help students with homework. Will afterschool staff just give students the answers? Not if they feel they are on the same team as school-day teachers.

• Allow the afterschool program to store materials in a corner of your classroom. For afterschool staff scrambling to set up makeshift learning spaces in someone else’s room, this is a godsend, and this courtesy greatly increases the chance that the classroom will be left in the same condition it was found. This support might be a rolling cart, plastic crates, or a cubby.

• Recognize the value of afterschool staff. “While they may not (yet) hold a degree or have the same background in pedagogy that you do,” says Meyers, “afterschool staff often have deep roots in the communities they work in. And they tend to come from and look more like the population of students being served than the teachers sometimes do.” These qualities need to be respected and integrated into the full experience of the students.

• Advocate for more funding for your school’s afterschool programs so staff can be paid better wages. Enough said.

“When we start to break down the barriers between ‘school day’ and ‘afterschool,’” concludes Meyers, “we are taking a giant step toward being a full service to our students and families.”

“The Rock Star You’re Ignoring: How Afterschool Staff Can Take Your Class to the Next Level” by Eva Jo Meyers in Cult of Pedagogy, January 19, 2020, https://bit.ly/2tLPrtx

5. Phonics Is Only Part of Good Literacy Instruction

In this Education Week article, Heidi Anne Mesmer (Virginia Tech University) says there’s strong research support for teaching four foundational reading skills in the early grades:

– Print concepts – for example, print runs left to right, words are groups of letters separated by a space;

– Phonological awareness – being able to orally identify and manipulate the sound units of language, including the alphabetic principle: that symbols represent speech sounds (cat equals three symbols, three sounds);

– Phonics and word recognition – the correspondence between visual symbols (graphemes made up of letters) and speech sounds (phonemes); this includes analyzing multisyllabic words, which means teaching morphology through fifth grade;

– Fluency – being able to read connected text accurately, and with proper expression (volume, phrasing, smoothness, and pace), with little conscious effort, conveying and being able to focus on the meaning.

The bad news, says Mesmer, is that many schools aren’t teaching all four in a thorough and balanced way, often putting too much emphasis on phonics. That prevents students from becoming proficient at automatically recognizing words and being able to devote most of their mental bandwidth to understanding complex ideas and vocabulary.

“No one can concentrate on Newton’s laws, plot development, or electrical circuits if they are struggling to decode every fifth word,” says Mesmer. “We are putting the cart before the horse if we drill letter/sounds without also teaching print concepts and the alphabetic principle… Can you imagine going to a job where you learn all about the different types of buttons, threads, fabrics, and zippers but no one tells you that you are manufacturing jeans? Yet that’s often how reading instruction can feel for children.”

“Simply put,” says Mesmer, “foundational skills cannot be separated. Print concepts and phonological awareness support phonics instruction, morphological instruction extends students’ word recognition, and fluency automatizes word reading.” She believes the schools that get the best (and the most equitable) results are following these precepts:

• Teaching the foundational skills systematically – This means a curriculum and materials that specify what is taught and in what sequence.

• Balancing the four skills – “These skills are complementary and need to be consistently taught, in response to development, through grade 5,” she says.

• Being explicit about key concepts – Mesmer recently tested more than 100 kindergarten students who knew about 90 percent of their letter/sounds but could not decode simple words. What was lacking was direct teaching of grapheme/phoneme relationships, word roots, and syllable patterns.

• Using assessment information to differentiate – Students entering kindergarten may know all their letter names or none. “Teachers must use simple diagnostic assessments that inform cumulative review and instruction, and often must use small-group instruction,” says Mesmer.

• Using high-quality, aligned materials – A recent RAND study found that only seven percent of elementary teachers were using at least one well-vetted set of ELA materials. EdReports.org has a tool that can zero in on the best materials.

• Seeing the bigger picture – Full literacy instruction includes vocabulary, world knowledge, comprehension, writing, and other Common Core standards.

“There Are Four Foundational Reading Skills. Why Do We Only Talk About Phonics?” by Heidi Anne Mesmer in Education Week, January 23, 2020, https://bit.ly/3aIfdPL; Mesmer can be reached at hamesmer@vt.edu,

6. Increasing Joy in Primary-Grade Math Classes

In this Mathematics Teacher article, teacher educator Amy Noelle Parks (Michigan State University) says that after 30 years as an educator, her criterion for excellence in primary-grade mathematics classrooms is joy. This is not the same thing as fun, says Parks: she’s talking about “flow” – children being so immersed in meaningful classroom activities that they lose track of time. Parks suggests five strategies for maximizing joy and minimizing anxiety and other negative emotions in math classes:

• Create space for play. “Play is a powerful tool for reducing stress and for increasing opportunities for mathematical learning,” she says – as long as the materials are well chosen. Some possibilities: counting collections, wooden or Lego blocks, puzzles, and linear board games.

• Allow children to make choices. Children are empowered and more likely to enjoy classroom activities when they can make decisions on how to spend time, who to spend it with, and which materials to use.

• Offer problems that include exploration, social interaction, and engaging materials. A problem might be a question – If the giant in Jack in the Beanstalk is ten times as tall as a person, how tall is he? – or a counting challenge, or a brain teaser. Enjoyment is increased if students can share their answers with classmates without fear of making a mistake.

• Relax a little about time on task. “The occasional off-task moment will not significantly interfere with children’s ability to learn mathematics,” says Parks. Teachers snapping their fingers and ordering students engaging in chit-chat to get back to work will definitely not contribute to joyful learning.

• Foster caring relationships. “Creating a welcoming environment draws on some classic early childhood teaching practices,” says Parks, “– greeting children with a smile and by name, taking time to get to know each child, and helping children to name and handle their emotions.” Risk-taking and joy are also promoted by including children’s interests, experiences, and home languages and cultures.

In addition to these joy-promoting practices, Parks suggests that teachers make the following choices:

– Ask children to tackle a few deep tasks versus doing dozens of similar computation problems;

– Allow children to talk versus telling them to work in silence;

– Focus on growth over time versus achievement against a standard;

– Emphasize fluency over speed;

– Provide a variety of instructional settings versus the same routine every day;

– Incorporate art, music, and science into math lessons versus a siloed approach.

“Creating Joy in PK-Grade 2 Mathematics Classrooms” by Amy Noelle Parks in Mathematics Teacher, January 2020 (Vol. 113, #1, pp. 61-64), https://bit.ly/38N36Px; Parks can be reached at parksamy@msu.edu.

7. Four-Text Sets to Build Students’ Reading Power

In this article in The Reading Teacher, Sara Lupo, Alicia Berry, Emma Thacker, Amanda Sawyer, and Joi Merritt (James Madison University) suggest the “Quad Text Set Framework” to meet the four challenges of elementary literacy instruction:

• Building students’ content knowledge – “Without knowledge,” say the authors, “learners struggle at every stage of the reading process, from decoding to fluency to making higher level inferences.”

• Motivating students to read – Teachers must tap students’ curiosity, and one way of doing that is developing a line of inquiry into an intriguing content topic.

• Reading challenging texts – “We cannot keep students who have been labeled as struggling from the benefits that challenging texts provide,” say the authors, “such as exposure to challenging concepts and ideas, rare and academic vocabulary, or complex syntax structures.” Teachers need to judge texts by students’ background knowledge, the level of abstractness, language formality, and cohesiveness.

• Reading accessible texts – Not everything has to be hard, say the authors; students need to be exposed to a variety of texts and media and know how to navigate them.

The Quad Text Set Framework guides teachers in selecting four texts on a topic that together build content knowledge, motivate students, provide challenging material, and enhance skills in navigating different kinds of texts:

– The target text has challenging content-area text on the topic being studied.

– An informational text is easier and builds content knowledge.

– A “hook” text shows the relevance of the topic or its real-world application.

– A visual text (a picture book or video) builds knowledge visually.

The teacher decides on the best sequence of the four texts.

Here are examples of quad text sets in different subject areas:

A fourth-grade science unit on electricity:

– Hook text: Because You’ll Never Meet Me by Leah Thomas

– Informational texts: What Happens When…? by John Farndon and Switch On, Switch Off by Melvin Berger

– Visual text: A video explaining how electrical circuits work (Explaining an Electrical Circuit)

– Target text: What Are Electrical Circuits? by Ronald Monroe

A second-grade social studies unit on civil rights activists challenging unfair laws:

– Hook text: Interactive readaloud of Boycott Blues: How Rosa Parks Inspired a Nation by Andrea David Pinkney and Brian Pinkney

– Visual text: A video about Rosa Parks that includes words and pictures

– Informational texts: Civil Rights Activists: Rosa Parks from Newsela and Here Is the Truth About What a Famous Black Bus Rider Did 60 Years Ago from Newsela

– Target text: I Am Rosa Parks by Rosa Parks with Jim Haskins

A first-grade math unit on halves and quarters:

– Hook text: The Cookie Fiasco by Dan Santat

– Visual text: a BrainPop Jr. video, “Basic Parts of a Whole”

– Informational text: Give Me Half by Stuart Murphy

– Target text: Pizza Pizzazz! by Carol Losi

“Rethinking Text Sets to Support Knowledge Building and Interdisciplinary Learning” by Sara Lupo, Alicia Berry, Emma Thacker, Amanda Sawyer, and Joi Merritt in The Reading Teacher, January/February 2020 (Vol. 73, #4, pp. 513-524), available for purchase at https://bit.ly/2O4Nm2D; Lupo can be reached at luposm@jmu.edu.

8. Recommended Storybooks and Audiobooks

In this article in Language Arts, Grace Enriquez, Mary Ann Cappiello, and Erika Thulin Dawes (Lesley University), and Katie Egan Cunningham (Manhattanville College) endorse and describe the following K-8 picturebooks and audiobooks (click on the link below for cover images and detailed descriptions, including two apps not listed below):

Picturebooks:

– The Wall in the Middle of the Book by Jon Agee (Dial, 2018)

– ¡Vamos! Let’s Go to the Market by Raúl the Third (Houghton Mifflin, 2019)

– Because by Mo Willems, illustrated by Amber Ren (Hyperion, 2019)

– Hey, Water! by Antoinette Portis (Neal Porter/Holiday House, 2019)

– Another by Christian Robinson (Atheneum, 2019)

– Good Boy by Sergio Ruzzier (Atheneum, 2019)

Audiobooks:

– Du Iz Tak? by Carson Ellis, narrated by Eli D’Amico, Sebastian D’Amico, Burton Fott, Galen Fott, Laura Fott, Sarah Hart, Bella Higginbotham, and Brian Hal (Weston Woods, 2018)

– Esquivel! Space-Age Sound Artist by Susan Wood, illustrated by Duncan Tonatiuth, narrated by Brian Amador (Live Oak Media, 2018)

– Spin: The Rumpelstiltskin Musical, music by Neil Fishman, book and lyrics by Harvey Edelman, performed by Jim Dale, Barrett Leddy, Lisa Livesay, Khristine Hvam, Nicola Barber, Nick Sullivan, John Brady, and Johnny Heller (HarperAudio, 2017)

– Wishtree by Katherine Applegate, narrated by Nancy Linari (Listening Library, 2017)

– The Night Diary by Veera Hiranandani, narrated by Priya Ayyar (Listening Library, 2018)

“Stories for Multimodal Learners: Picturebooks, Audiobooks, and Apps to Engage K-8 Students” by Grace Enriquez, Mary Ann Cappiello, Katie Egan Cunningham, and Erika Thulin Dawes in Language Arts, January 2020 (Vol. 97, #3, pp. 186-193), https://bit.ly/2RyOvBT

9. Short Items:

a. Impeachment teaching resources – This Education Week article by Stephen Sawchuk https://bit.ly/2RQPg8g has extensive resources for upper-grade classes covering the current impeachment debate, along with pointers for handling a controversial topic.

“Teaching Impeachment? Here’s Your One-Stop Shop for Resources” by Stephen Sawchuk in Education Week, October 10, 2019

b. A video on probability – This video by Leonardo Barichello can serve as an introduction to teaching probability: https://www.youtube.com/watch?v=Kgudt4PXs28&

“The Last Banana: A Thought Experiment in Probability” by Leonardo Barichello, February 23, 2015, spotted in “Is the Last Banana Game Fair?” by Patrick Sullivan in Mathematics Teacher, January 2020 (Vol. 113, #1, pp. 33-38), available to NCTM members at

https://pubs.nctm.org/view/journals/mtlt/113/1/article-p33.xml

 
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