James Baldwin on American History

 American history is 

longer, larger, more

various, more beautiful,

and more terrible than

anything anyone has

ever said about it.

James Baldwin

What Kinds of Mathematics Do Students Need for the Real World?

        In this article in Mathematics Teacher: Learning & Teaching PK-12, Jo Boaler, Tanya LaMar, and Cathy Williams (Stanford University) report on a project that started with a phone call Boaler received from Steve Levitt of Freakonomics fame. Levitt had been helping his own children with their high-school mathematics homework and was struck by what he considered the antiquated nature of the work they were doing. Very little of it, he said, was the kind of math that he used in his professional and personal life. 

         To check this perception with a wider group, Levitt and his colleagues at the University of Chicago did a survey of visitors to the Freakonomics website asking what kinds of math they used on a daily basis, and 913 people responded. Boaler, LaMar, and Williams saw the results and noticed that almost 3/4 of the respondents were men, so they asked the same questions of education leaders; 427 responded, mostly women. Strikingly, the responses from the two groups were quite similar. Here are the percentages in each group saying they used each kind of mathematics “daily”: 

                                                   Freakonomics                  Educators 

- Use Excel/Google sheets                66                                56 

- Access and use databases                42                               37 

- Analyze and interpret data              31                                21 

- Visual data                                      23                                12 

- Algebra                                           11                                  4 

- Geometry                                         4                                   0 

- Calculus                                           2                                   1

- Trigonometry                                   2                                   0 

The percentages who said they “never” used algebra, geometry, calculus, and trigonometry were 28, 50, 70, and 79 respectively for the Freakonomics group and 41, 59, 71, and 82 for the educators. 

        Clearly these adults don’t use much of the math they learned in school – but they do make heavy use of data knowledge and tools. “For generations,” say Boaler, LaMar, and Williams, “high schools in the United States have focused on one course as the ultimate, college-attractive, and high-level course – calculus. This has led to a heavy focus on algebraic content in the earlier years even though a tiny proportion of students in the school system take calculus. When students do take calculus, it is often taken after rushing through years of content without the development of deep understanding.” And most students who take calculus in high school end up repeating it in college, or taking a lower-level course.

        The Common Core standards put more emphasis on data and statistics – but not enough, say the authors, which is why some states, including California, are beefing up data literacy in their curriculum standards. In that spirit, the Stanford and University of Chicago teams joined with colleagues around the world and spent 18 months thinking through what needs to change. “It quickly became clear,” say Boaler, LaMar, and Williams, “that all students – starting from the youngest in prekindergarten to those in college – need to learn the mathematics that will help them develop data literacy, to make sense of the data-filled world in which we all live… Whatever job your students go into, they will be making sense of data… Data awareness and data literacy are needed to not only be an effective employee but also function in the modern world… If we do not help students become data literate, they will be vulnerable to people who are misrepresenting issues and data.” 

        This line of thinking has spawned an initiative called YouCubed; the website has had more than 51 million visitors so far. It includes a series of “data talks,” which show students a data representation and ask, What do you notice? and What do you wonder? Among the topics: basketball, endangered species, popular dogs, and data ethics. Here’s an example of a middle-school data talk (see the article link below for more). Naturally, Boaler, LaMar, and Williams advocate a K-12 curriculum with an alternative pathway focused on data science and statistics. “Research suggests that the content of such a pathway is much more engaging for broader groups of students,” they say, “providing more-equitable participation in higher-level courses.” 

 “Making Sense of a Data-Filled World” by Jo Boaler, Tanya LaMar, and Cathy Williams in Mathematics Teacher: Learning & Teaching PK-12, July 2021 (Vol. 114, #7, pp. 508-517); the authors can be reached at joboaler@stanford.edu, tlamar@stanford.edu, and cathyw11@stanford.edu.

Please Note: This summary is reprinted with permission from issue #897 of The Marshall Memo, an excellent resource for educators.

How Effective is Orton-Gillingham?

        In this article in Exceptional Children, Elizabeth Stevens (Georgia State University), Clint Moore, Nancy Scammacca, Alexis Boucher, and Sharon Vaughn (University of Texas/Austin), and Christy Austin (University of Utah) report on their meta-analysis of 16 studies of Orton-Gillingham, a popular and widely used approach to reading instruction. Orton- Gillingham is described as a “direct, explicit, multisensory, structured, sequential, diagnostic, and prescriptive” method for teaching children with (or at risk for) word-level reading disabilities, including dyslexia. 

        The researchers’ conclusion: although the mean effect size (0.22) was positive and somewhat promising, Orton-Gillingham did not substantially improve children’s phonological awareness, phonics, fluency, spelling, vocabulary, and reading comprehension. “Despite the continued widespread acceptance, use, and support for Orton-Gillingham instruction,” conclude Stevens et al., “there is little evidence to date that these interventions significantly improve reading outcomes for students with or at risk for word-level reading disabilities over and above comparison group instruction.” 

        This finding certainly raises concerns about the fact that a number of states have adopted legislation mandating Orton-Gillingham. “More high-quality, rigorous research with larger samples of students with word-level reading disabilities,” say the authors, “is needed to fully understand the effects of Orton-Gillingham interventions on the reading outcomes of this population.” 

 “Current State of the Evidence: Examining the Effects of Orton-Gillingham Reading Interventions for Students with or at Risk for Word-Level Reading Disabilities” by Elizabeth Stevens, Christy Austin, Clint Moore, Nancy Scammacca, Alexis Boucher, and Sharon Vaughn in Exceptional Children, July 2021 (Vol. 87, #4, pp. 397-417); Stevens can be reached at estevens11@gsu.edu.

Please Note: This summary is reprinted with permission from issue #897 of The Marshall Memo, an excellent resource for educators.

What is the Purpose of Mathematics?

        In this article in Mathematics Teacher: Learning & Teaching PK-12, Lucy Watson (Belmont University) and Christopher Bonnesen and Jeremy Strayer (Middle Tennessee State University) describe a common dilemma for math teachers: what do you say when students ask, Why do I need to know that? Some teachers point to practical, real-life applications in science, technology, engineering, and math education. Others extoll the beauty and wonder of mathematics. What teachers say might reveal one of three views of the nature of mathematics: 

        - It’s a set of facts, rules, and tools that need to be memorized; 

        - It’s a static body of knowledge bound by discovered truths that never change; 

        - It’s a dynamic, problem-driven discipline defined by creativity, inquiry, and openness to revision. Students taught by a teacher holding each view will learn mathematics quite differently, and will likely be exposed to distinct teaching methods, from rote lectures to discussions and hands-on projects.          

        Watson, Bonnesen, and Strayer believe there hasn’t been enough guidance for math teachers on exactly what the nature of mathematics is, leaving the field wide open to a variety of rationales – and probably some pretty dull teaching. Drawing on several guiding documents in the field, the authors suggest this five-point view of the nature of mathematics: 

        • Mathematics is a product of the exploration of structure and patterns. 

        • Mathematics uses multiple strategies and multiple representations to make claims. 

        • Mathematics is critiqued and verified by people within particular cultures through justification or             proof that is communicated to oneself and others. 

        • Mathematics is refined over time as cultures interact and change. 

        • Mathematics is worthwhile, beautiful, often useful, and can be produced by each and every                         person. 

         The authors believe that as students grapple with high-quality math problems, teachers should get them thinking about this broader view of the nature of mathematics, asking students about purpose before, during, and after solving the problems. Watson, Bonnesen, and Strayer suggest repeating this meaning-seeking activity at intervals through the grades – perhaps with a unit on counting in kindergarten, equivalent fractions in third grade, area relationships in middle school, and absolute value in high school. If this occurs, say the authors, teachers will less frequently hear the question, Why do I need to know that? 

 “The Nature of Mathematics: Let’s Talk About It” by Lucy Watson, Christopher Bonnesen, and Jeremy Strayer in Mathematics Teacher: Learning & Teaching PK-12, May 2021 (Vol. 114, #5, pp. 552-561); the authors can be reached at Lucy.watson@belmont.edu, ctb4d@mtmail.mtsu.edu, and jeremy.strayer@mtsu.edu.

Please Note: This summary is reprinted with permission from issue #888 of The Marshall Memo, an excellent resource for educators.

"Learning Loss" - Wrong and Right Solutions

        In this online article, Harvey Silver and Jay McTighe worry that “lost learning” is an unfortunate way to define the challenge schools face as they reopen for in-person instruction. By framing the challenge as instructional time lost, there’s a tendency to think the solution is rapidly covering the curriculum that students missed – which has two downsides. “At the classroom level,” say Silver and McTighe, “this solution could take the form of cutting out any of those time-consuming learning activities such as discussions, debates, hands-on science investigations, art creation, and authentic performance tasks and projects” – instead “trying to blitz through lots of factual information.” 

        Rather than focusing on the content that wasn’t covered during remote and hybrid instruction, they propose two more-productive approaches: 

        • Prioritizing the curriculum on outcomes that matter the most – A simple but effective way to accomplish this is preceding the title of each curriculum unit with the words, A study in… Several examples: 

        - The calendar – A study in systems 

        - Linear equations – A study in mathematical modeling 

        - Media literacy – A study in critical thinking 

        - Any sport – A study in technique 

        - Argumentation – A study in craftsmanship 

Preceding a unit title with those three words, say Silver and McTighe, “establishes a conceptual lens to focus learning on transferable ideas, rather than isolated facts or discrete skills.” 

        It’s also helpful to frame the unit around Essential Questions. For the five units above, here are some possibilities: 

        - How is the calendar a system? What makes a system a system? 

        - How can mathematics model or represent change? What are the limits of a mathematical model? 

        - Can I trust this source? How do I know what to believe in what I read, hear, and view? 

        - Why does technique matter? How can I achieve maximum power without losing control? 

        - What makes an argument convincing? How do you craft a persuasive argument? 

Well-framed Essential Questions are open-ended, stimulate thinking, discussions, and debate, and raise additional questions. 

        • Engaging learners in deeper learning that will endure – “To learn deeply,” say Silver and McTighe, “students need to interact with content, e.g., by linking new information with prior knowledge, wrestling with questions and problems, considering different points of view, and trying to apply their learning to novel situations.” The most important skills are comparing, conceptualizing, reading for understanding, predicting and hypothesizing, perspective-taking, and exercising empathy. 

        A kindergarten example: challenging students to predict how high they can stack blocks before a tower falls down, then having them try different hypotheses and see what works best, and note the success factors. “This focus on cause and effect will become a yearlong inquiry for students,” say Silver and McTighe, “as they learn to use it to examine scientific phenomena, characters’ behavior in stories, and even their own attitudes and motivations as learners.” (The full article, linked below, includes a middle-school unit on genetically modified food and a high-school unit comparing the educational philosophies of Booker T. Washington and W.E.B. DuBois.) 

        This two-part approach to curriculum is not just “a stopgap measure tied to current anxieties about learning loss,” conclude Silver and McTighe: “Framing content around big ideas and actively engaging students in powerful forms of thinking is good practice – in any year, under any conditions.” 

“Learning Loss: Are We Defining the Problem Correctly?” by Harvey Silver and Jay McTighe on McTighe’s website, May 7, 2021; McTighe can be reached at jmctigh@aol.com.

Please Note: This summary is reprinted with permission from issue #886 of The Marshall Memo, an excellent resource for educators.

Online Groups for School Leaders

         In this article on The Main Idea website, Jenn David-Lang says school leaders are hungry for professional development, but receive less than other educators – which may explain some of the attrition we’re seeing among administrators. While schools were closed during the pandemic, David-Lang had an idea: why not involve groups of administrators in Masterminds, an online version of accountable, results-focused teacher PLCs? The term Masterminds was coined almost 100 years ago by author Napoleon Hill, but has only recently found its way into the world of K-12 schools. 

        Here’s how David-Lang and her colleague Mitch Center have implemented the concept. They’re running several year-long Mastermind groups, each with about eight school- and district-based leaders from varied locations (“from Baltimore to Bangkok,” says David-Lang). Groups meet twice a month via Zoom to learn new ideas, share strategies, solve problems, and support one another. The one-hour meetings go quickly, following this structure: 

    • Check-ins – Everyone briefly shares a struggle or a win. “Getting an inside view of how everyone is doing and what is going on at each other’s schools builds trust,” says David-Lang; “principals are rarely given space to share how they’re honestly doing without the need to put on their ‘principal face.’” 

        • Goal sharing – In two-person breakout rooms, members report on a goal they committed to in a shared Google Doc at the end of the previous session. This provides continuity from meeting to meeting and keeps people accountable for actions to which they have committed. 

         • New content – David-Lang and Center share a one-page summary of ideas or research on their screens and everyone reads it silently. A recent example: a synthesis of five mindset shifts described in a recent book on unconscious bias by Sarah Fiarman and Tracey Benson. David-Lang and Center then facilitate a discussion of the ideas, sometimes regrouping into two breakout rooms, or participants fill out a shared graphic organizer. 

         • Think tank – One member presents a real-life dilemma, including the background and context of the problem (one example: dealing with a new assistant principal who is not garnering respect from colleagues). Other members ask clarifying questions, and then the presenter remains silent while the rest of the team discusses the issue and suggests possible solutions. Finally, the presenter recaps those ideas and thinks out loud about the ones that seem most likely to work. 

        • One Big Thing (OBT) – In the Chat area, there’s a link to a shared Google Sheet with a row for each member, and they write their biggest takeaways from the session. This makes available to everyone the collective learning from the reading, discussion, and problem-solving. This segment was inspired by John Dewey’s insight that true understanding comes not from doing, but from reflecting on what’s been done. 

        • Committing to a goal. Each session ends with each member writing a commitment for specific action, to be reviewed at the beginning of the next meeting. 

        Reflecting on a year of leading Mastermind groups, David-Lang looked up the criteria for effective professional development compiled by Linda Darling-Hammond and colleagues. It turned out that her groups were meeting every one of them:

• Focused on content;
• Incorporating active learning; 
• Supporting collaboration; 
• Using models of effective practice; 
• Providing coaching and expert support; 
• Offering opportunities for feedback and reflection; 
• Sustained over time. 

 “While my co-facilitator and I have coached school leaders individually,” says David-Lang, “we were immediately struck by the exponential power of coaching that comes from all members sharing their own learned strategies and diverse perspectives… It is the collective wisdom, energy, and passion that truly distinguishes Masterminds from other forms of PD for educational leaders.” 

         While the sessions have been particularly valuable during the disruptions of the pandemic, David-Lang believes they should continue to be an important forum in the new normal. 

 “Masterminds: When PL Meets PLC” by Jenn David-Lang, The Main Idea, May 2021; David-Lang can be reached at Jenn@TheMainIdea.net. 

 Please note: This summary was reprinted with permission from issue # 886 of the Marshall Memo, an excellent resource for educators.

Four Key Teacher Roles in a Personalized Classroom

           In this Elementary School Journal article, Penny Bishop, John Downes, Steven Netcoh, Katy Farber, Jessica DeMink-Carthew, Tricia Brown, and Rachel Mark (University of Vermont) report on their interviews with a number of elementary and middle-school teachers on personalized learning.  The researchers define personalization "as an approach that encourages partnership between individual students and teachers in the design of learning that emerges from students' interests, questions, needs, and preferences to foster self-directed learning."  Assessments may take the form of portfolios of student work, authentic performance tasks, and exhibitions of learning in which students demonstrate their skills and understandings.

          Teachers in the study described the shift from running adult-centered classrooms to supporting students as they brought their interests, needs, and different levels of readiness to the classroom.  One teacher drew a distinction between personalization and individualization, the latter being about getting all students "to arrive at the same spot through different means."

          Synthesizing what they learned from interviews, the researchers identified four roles teachers played in personalized classrooms:

• Empowerer - Teachers sought to increase students' independence and ownership of learning by letting them lead, offering choices, enabling students to work at their own pace and level, increasing student talk, and learning with and from students.

• Scout - Teachers often needed to seek out resources to support students and figure out next steps in their learning progressions.  This involved ascertaining students' interests, aligning the curriculum with those interests, curating digital and material resources, and connecting students with helpful people inside and outside the school.  "We can't offer everything," said one teachers, "but it's not our job to offer everything.  It's our job to explain how to navigate the world."

• Scaffolder - Teachers constantly worked to ensure that students engaged productively in learning.  This involved structuring routines, time, and learning experiences, fading the support when students didn't need as much, modeling possible approaches, and asking questions.  "Okay," said one teacher to her students, "you have your team leaders. You have your roles.  You can do it.  Sign up on the board if you need my help." She then "floated" around the room.

• Assessor - Teachers said it was important to distinguish between assessment and evaluation (with the latter, offering lots of narrative feedback to students,) provide ongoing formative assessment (a lot of over-the-shoulder checking for understanding and redirection) and be clear about learning targets and rubrics posted around the room.

"Teacher Roles in Personalized Learning Environments" by Penny Bishop, John Downes, Steven Netcoh, Katy Farber, Jessica DeMink-Carthew, Tricia Brown, and Rachel Mark in Elementary School Journal, December 2020 (Vol. 121,#2, pp. 311-336); Bishop can be reached at Penny.Bishop@uvm.edu.

(Please Note: The summary above is reprinted with permission from issue #871 of 

The Marshall Memo, an excellent resource for educators.)