In This Issue:

1. Ten reasons discovery learning continues to be popular

2. When should students take Algebra I?

3. The secret sauce of seven highly effective Utah math teachers

4. Teaching writing in the AI era

5. Helping students tackle multi-step assignments

6. Douglas Reeves on getting grading reform unstuck

7. Graphic novels on families

 

Quotes of the Week

“Falling behind is simply not an option.”

            A Utah middle-school math teacher (see item #3)

 

“Ask a trusted friend, ‘What’s one thing I need to hear, but probably don’t want to?’”

            Dan Rockwell in “The 7 Universal Laws of the Rut” in Leadership Freak, May 7, 2025

 

“In reading, foundational skills typically refer to students’ learning how to ‘crack the code’ of recognizing the sounds in English and how they’re mapped onto letters. But skilled reading includes more than just these word recognition elements. Students must also learn the structures of written English, to read with increasing fluency, and to draw on their background knowledge and expanding vocabulary to understand what they read.” 

            Sarah Sparks in “Are Early-Reading Laws Changing Teaching Practices?” in Education 

Week, April 25, 2025; Sparks can be reached at [email protected].

 

“When a measure becomes a target, it ceases to be a good measure.”

            Goodhart’s Law (1975) – that a metric originally designed to measure a system’s 

performance, if turned into a goal, can distort and undermine the original purpose of the 

measure. Examples: a focus on test scores leading to overuse of test prep; DIBELS scores leading to an overemphasis on reading quickly and practicing nonsense words.

 

“Our relationships with our smartphones are far from healthy. The mediascape is becoming a stormy sea of anxiety, envy, delusion, and rage. Our attention is being redirected in surprising and often worrying ways. The overheating of discourse, the rise of conspiratorial thinking, the hollowing out of shared truths: all these trends are real and deserve careful thought. The panic over lost attention is, however, a distraction… Ours is an era of obsession as much as distraction, of long forms as much as short ones, of zeal as much as indifference. To ascribe our woes to a society-wide attention deficit disorder is to make the wrong diagnosis.”

 

 

 

 

 

 

1. Ten Reasons Discovery Learning Continues to be Popular

            In this online article, psychologist Paul Kirschner traces the historical roots of discovery learning:

• The romantic ideal of learning – Jean-Jacques Rousseau and his followers argued that children learn best when they interact with nature and engage in real-world experiences, exploration, and discovery. Educators and parents in this tradition believe children are naturally curious and are capable, in the right conditions, of constructing knowledge independently. “This romanticized idea,” says Kirschner, “is deeply ingrained in educational thought and resists empirical challenges.” 

            • The progressive movement – John Dewey and others inspired a movement holding that learning should be student-centered and driven by children’s natural curiosity and democratic values – and critical of rote memorization and instruction in which students were seen as passive sponges. “These ideas became deeply embedded in teacher education,” says Kirschner. “Terms like ‘guide on the side’ vs. ‘sage on the stage’ were popularized, reinforcing the idea that teachers should step back.” 

            • Anti-authority sentiment – Discovery learning is allied to cultural and philosophical mistrust of hierarchical control, centralized expertise, and imposed knowledge. Thought leaders like Paulo Freire and Ivan Illich portrayed traditional education as a means of social control, viewing teachers with suspicion and mistrust. “From this perspective,” says Kirschner, “explicit instruction became equated with indoctrination, while discovery learning was seen as a path to emancipation… In this cultural context, discovery learning isn’t just a teaching method. It becomes a symbol of freedom, self-determination, and resistance to authority.” 

            • Cultural and political appeal – Self-directed learning resonates with the values of independence, creativity, innovation, personal growth, self-reliance, and breaking free of outdated traditions – values that are prized in western societies. This points to repositioning the teacher from authority figure to facilitator, with children constructing their own understanding rather than being told how the world works. 

   All this explains the continuing appeal of discovery learning, but Kirschner reports that it has not stood up well as researchers have documented what works best in classrooms. Strong empirical evidence, he says, shows that explicit, teacher-guided instruction is better than discovery learning in three ways:

-       It’s more effective – students learn more.

-       It’s more efficient – it takes less time and mental effort.

-       It’s more fulfilling – students feel successful and are motivated to learn more. 

Given the research track record, why does discovery learning continue to have so much support? Kirschner offers several explanations:

            • Overgeneralizing success stories – It’s true that some students thrive in a discovery-based learning environment, says Kirschner – “especially those who are already highly motivated and have a strong foundation of prior knowledge.” But these students are not representative of the general student population, including many in under-resourced communities. 

            • Confirmation bias – People tend to favor information that confirms “their existing beliefs, expectations, and assumptions,” says Kirschner, “while ignoring or downplaying evidence that contradicts them.” This can happen when educators see some success with discovery-based approaches, selectively remembering those successes and overlooking things that didn’t work out as well. 

            • The illusion of understanding – While students are engaged and working hard with discovery learning, it can feel like they’re learning deeply – but they may be reaching incorrect solutions and buying into misconceptions. Students may feel like they “get it” because of the effort they’ve put in, and may be resistant to correction, even if they get timely feedback. 

            • The constructivist teaching fallacy – It’s true that people learn best by integrating new information into their existing knowledge structures. But when teachers provide only minimal guidance, students may not have enough information to construct coherent knowledge.

            • The appeal of active learning – Research shows that active learning enhances retention, but if students use trial and error to solve a problem, they may have no idea how they got there. “Well-guided discovery and explicit instruction can still be highly interactive and engaging,” says Kirschner.

            • Treating students as experts – The idea behind discovery learning is that since scientists and other experts work through discovery, students can learn that way too. But experts see the world differently than novices, bringing to bear extensive background knowledge and mental models that guide them as they wrestle with problems. “Scientists do science,” says Kirschner. “Students learn science.” 

“Studies in cognitive science,” Kirschner concludes, “consistently demonstrate that students learn best when they’re first explicitly taught foundational concepts before engaging in problem-solving or exploration. Scaffolding and well-designed instructional sequences allow students to explore and apply knowledge meaningfully after they have been given the necessary tools. This doesn’t mean that learning should be passive. Well-designed instruction incorporates active engagement, inquiry, and critical thinking, but within a framework that provides necessary support.” 

 

“The Seductive Appeal of Discovery Learning” by Paul Kirschner, March 30, 2025

 

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2. When Should Students Take Algebra I?

            In this Annenberg Institute/Brown University report, Elizabeth Huffaker (Stanford University) addresses three much-discussed issues with Algebra I: access, grouping, and supports:

            • Access – Algebra I is a key gatekeeper to advanced math coursework, college enrollment, STEM careers, and long-term economic outcomes. Students who are not proficient in Algebra I by the end of 9^th grade are less likely to meet college admissions requirements – and the course has the highest failure rate in the first year of high school. To be on track to take Calculus in high school, it’s preferable to take Algebra I in 8^th grade, but many students are not ready to be successful in the course at that point. 

            Whether students take Algebra I in middle or high school is determined by four factors, says Huffaker:

-   Readiness – Students enter middle school with a wide range of skills and knowledge, with low-income students and students of color having the biggest skill deficits.

-   Bias in placement – Referrals by teachers and counselors may be tilted by unfair assumptions about some students’ ability to handle Algebra I.

-   Information and preferences – Some students don’t have role models, encouragement, and accurate information on why they should take Algebra I.

-   Availability – Rural middle schools are less likely to offer the course.

In 1986, only 15 percent of U.S. 8^th graders took Algebra I, with wide variation among schools. The “Algebra for All” movement in the 1990s and 2000s led many schools to expand access to Algebra I in middle school, but failure rates jumped and test scores sank. 

Common Core standards contained higher expectations for middle-school math, which led (along with concerns about equity) to some districts deferring Algebra I to 9^th grade. This led to backlash among parents who felt their children were being held back. By 2024, middle-school Algebra I enrollment had more than doubled to 36 percent, with wide variation among states. Huffaker’s observations:

-   For students who are “algebra-ready” in middle school, taking Algebra I in 8^th, 7^th, or even 6^th grade leads to higher math achievement and opportunities down the road. 

-   In rural and low-SES schools, online courses give prepared students opportunities they might not otherwise have.

-   For borderline-ready students, taking Algebra I in middle school has mixed results, the key factors being tutoring and other supports and most classmates being proficient, so peer support boosts marginal students. 

-   Students who do not have the prerequisite math skills struggle with middle-school Algebra I and need lots of support.

How to maximize the number of middle-school students taking and succeeding in Algebra I and address equity issues? Huffaker suggests:

-   Prepared students should be able to take the course in 8^th grade.

-   Adopt an auto-enrollment policy in which prepared students are automatically enrolled in Algebra I, with parent opt-out available.

-   Students with skill gaps should take Algebra I in 9^th grade (with good support). 

-   Use test scores rather than subjective recommendations to place students. 

Free assessment tools like the Mathematics Diagnostic Testing Project are helpful, as are a number of formative assessments.

            • Grouping – Huffaker shares research on heterogeneous versus homogeneous student grouping. Forming classes based on students’ achievement levels (a.k.a. tracking) enables more-targeted instruction “and can benefit both middle- and high-achieving students,” she says. “But they also tend to widen achievement gaps, increase segregation, and can create negative self-perceptions for students in the lower-achieving class sections.” 

There are three additional concerns with homogeneous grouping. Teachers can unconsciously have lower expectations of the lower groups; sometimes less-qualified, less-experienced, and less-effective teachers are assigned to the lower tracks; and there tend to be more classroom management and disruption challenges in low-track classes. 

For schools with tracked math classes, the way students are grouped is important. “When schools use recent, multiple measures of achievement, such as predictive placement models or composite readiness scores,” says Huffaker, “and revisit placement decisions regularly, tracking can help ensure students receive instruction at the right level and pace.” High-achieving African-American and Latin students especially benefit from being placed in top math classes. 

But rigid tracking that starts in early grades is problematic, reinforcing existing opportunity gaps. And using a single outdated test score, teacher recommendations, or parental pressure can lead to unfair sorting, opportunities denied, and widening achievement gaps. 

            Mixed-achievement grouping (a.k.a. detracking) has pros and cons, Huffaker reports. Ideally, all students are exposed to the same high expectations, and lower-achieving students will benefit from working shoulder-to-shoulder with higher-achieving classmates, gaining in confidence and motivation. 

But this depends on teachers skillfully handling a wide range of achievement, orchestrating group projects, differentiation, use of formative assessments, peer dynamics, and maintaining high expectations for all. Whole-class teaching to the middle is more common, leaving some students under-challenged and others frustrated and falling further and further behind. Detracked math classes have also sparked complaints from parents who believe their high-achieving children are not being sufficiently challenged. 

            In short, says Huffaker, “effectively supporting a wide range of academic proficiency levels in one classroom requires teachers to have advanced skills, sufficient planning time, and access to strong instructional resources.” 

            • Supports – “Students learn best at their ‘learning edge’,” she says, “the space between what they can accomplish independently and what they can do with expert support.” The following practices help students get to that sweet spot:

-   Double-dose algebra, with two math classes a day, one providing just-in-time remediation on foundational concepts (the trade-off is less access to electives).

-   Staggered math blocks (not back-to-back), allowing for spaced practice, which improves student retention.

-   Small-group tutoring delivered multiple times each week, during the school day, by a well-supported tutor using high-quality instructional materials.

-   Online platforms (like IXL and ALEKS) and generative AI have the potential to deliver personalized, real-time math instruction, but they are as yet unproven and require skillful implementation. 

-   Summer bridge programs can help students build the math and study skills needed to be successful in Algebra I. Fractions, decimals, and rational numbers need special emphasis. 

Huffaker concludes with a list of several practices that schools should avoid:

-   Placing all students in the same math course at the same time.

-   Delaying Algebra I for all students, or accelerating students without strong supports.

-   Educators, parents, and students seeing Algebra I as a “status symbol” and a sign of overall intelligence, academic worth, and prestige. 

-   Evaluating Algebra I solely based on pass rates; initial struggles can be overcome.

-   Focusing narrowly on Algebra I as a measure of math success, which can distract from other key issues – improving K-5 math instruction, high-school math expectations, and the question of Calculus versus Statistics.

Finally, says Huffaker, Algebra I tracking “can unintentionally lock students into rigid groups across subjects, which amplifies the negative consequences of tracking for social integration… limiting valuable cross-class friendships and access to broader learning experiences.” 

 

“Evidence-Based Practices for Algebra I Access, Placement, and Success” by Elizabeth Huffaker, Annenberg Institute/Brown University, May 2025

 

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3. The Secret Sauce of Seven Highly Effective Utah Math Teachers

            In this article in Middle School Journal, Tye Campbell (Utah State University) and Jordan Green (Utah State Board of Education) report on their study of seven middle-school math teachers in high-poverty schools who consistently got impressive student learning gains. Here are the practices that struck Campbell and Green as they analyzed these teachers’ work in light of research on effective teaching: 

            • Team planning – Teachers met daily or weekly with colleagues to create lesson plans, design common assessments, anticipate student misconceptions, celebrate successes, and talk through failures. Some of the teachers in the study didn’t have common planning time and had to do their team planning over lunch or after hours. Campbell and Green urge principals to schedule team planning time at least once a week.

            • Mapping the curriculum – Teachers worked with their team to decide which math topics were most important and how much time to spend on each one, based on Utah standards, curriculum guides, and RISE assessments.

            • Attending to affect – Teachers regularly checked in on students’ emotional wellbeing, including their previous attitude toward mathematics. They explained and advocated for a growth mindset.

            • Mixed pedagogy – Teachers used a combination of direct instruction, partner and group problem-solving, peers-helping-peers, and enough time for practice. Some teachers used the traditional I do/you do/we do lesson sequence, others used launch/explore/discuss, with direct instruction coming after students tackled challenging work.

            • Whiteboards – Teachers had students solve problems on whiteboards rather than with pencil and paper, and used students’ whiteboard work to check for understanding and fix learning problems in real time.

            • Practicing without over-practicing – Teachers had students practice math skills, but kept the number of problems to a reasonable number. In most classes, homework usually took only 15 minutes.

            • Data-driven reteaching – Teachers used students’ work on short bellringer problems, class assignments, and unit assessments to decide whether and how to reteach certain concepts. Students scoring below mastery worked in Tier 2 groups.

            • Insisting on re-dos – Students had to keep working on assignments until they reached mastery (80 percent). One teacher said, “Falling behind is simply not an option.”

            Campbell and Green note that the instructional practices used by these star teachers are not in perfect alignment with common research findings on good teaching. Specifically, the teachers in this study did more direct instruction and had their students do more practice than is recommended by some researchers. “Policymakers might place more emphasis on practitioners’ perspectives when drafting policy documents,” say the authors, “particularly those who demonstrate exceptional success in their classrooms.” 

            

“Effective Mathematics Instruction in High-Poverty Middle Schools: What Are the ‘Best’ Teachers Doing?” by Tye Campbell and Jordan Green in Middle School Journal, May 2025 (Vol. 56, #3, pp. 9-24); the authors can be reached at [email protected] and [email protected]. 

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4. Teaching Writing in the AI Era 

            Based on two years studying the classroom impact of generative artificial intelligence, former middle- and high-school English teacher Eric Hudson says, “I have seen nothing to convince me that writing is an obsolete skill, no longer worth learning.” He suggests six core principles:

            • Writing matters. Studies show that learning to write well has cognitive, social-emotional, and civic benefits; that’s because it is both rigorous and deeply personal. What matters most for K-12 students, Hudson believes, is the process of composition. He quotes from a 2007 Carnegie Foundation report: “If students are to make knowledge their own, they must struggle with the details, wrestle with the facts, and rework raw information and dimly understood concepts into language they can communicate to someone else.”

            • The way we write is changing. Hudson believes we’re in the “post-plagiarism era,” and what’s emerging is a hybrid writing partnership between humans and artificial intelligence. Thinking in terms of preparing students for AI-infused jobs is the wrong approach, he says, because we don’t know what workplace technology will look like even a few years from now. “I think we should be engaging students in AI because of what’s happening now,” says Hudson, “not because of what might happen.” 

Right now, students and educators are figuring out how to use AI at every stage of the writing process, including “training AI bots on previous examples of their work, uploading notes and other artifacts to tailor the content of their writing, and using AI-generated feedback to make revisions.” A lot of this is flying under the radar because few schools have thought through what is okay and what needs to be punished or shamed. We must acknowledge that the act of writing is changing, he says, and at the same time uphold its essential value.

• Doing nothing is the riskiest choice. The worst scenario is students submitting work generated by AI and teachers using AI to grade it. If that happens, says Hudson, it’s a sign that students and teachers don’t care much about the work and are willing to settle for mediocrity. That’s most likely to happen if schools don’t have a frank discussion about AI and get the key issues out in the open. The goal: making the best use of low-tech and high-tech strategies so students’ writing is “relational and effortful,” involving “joy and investment,” and teachers are giving high-quality, personalized feedback.

• Having students do their writing in class is not the solution to AI cheating. “I am regularly surprised by the number of writing teachers who have responded to generative AI by simply moving all student writing into class,” says Hudson. “We have spent decades in education trying to move away from the high-stakes, low-validity environments that time-based assessments can create… Moving all writing into class is a pedagogical move that limits both students’ ability to write freely and our ability to assess writing.” 

How about using AI detectors to bust students who use bots to do their writing? Hudson believes that won’t work; it will lead to an endless “arms race” with teachers always one step behind ingenious students. The best strategy, he says, is to embrace some truly productive ways to use AI and insist on process, making all the stages of students’ writing “more visible and more explicit, whether or not AI is part of the process.” 

• The answer to a technological disruption is not necessarily more technology. The happy medium, Hudson believes, is to keep the focus on assessing student learning, however much they use artificial intelligence. “By insisting on process,” he says, “we give students the responsibility to document their process, compose writing, and reflect on their work.” Some possible steps:

-   Students launch writing projects with in-class writing.

-   Teachers incorporate oral defenses by students, or process portfolios.

-   Students who use AI as part of the process share transcripts of interactions.

-   Students reflect on what makes good writing and assess AI against those criteria. 

Hudson says this instructional evolution is analogous to the way math teachers tell students which homework problems and assessments are “calculator free” and in which they can use calculators. World language teachers have made a similar shift in the way their students interact with Google Translate and Duolingo. Writing teachers need to mix low-tech and high-tech strategies that get students deeply engaged in their own thinking and writing.

            • As we adjust to AI in real time, let’s keep our eye on the future. Hudson quotes three questions posed by Kathleen Blake Yancey in 2009 when online writing and social media were just emerging:

-   Develop new models for composing.

-   Design a new curriculum that supports those models.

-   Create new pedagogies that enact that curriculum. 

Hudson believes these apply equally well to the new challenges posed by artificial intelligence. 

 

“AI and the Teaching of Writing” by Eric Hudson, April 27, 2025

 

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5. Helping Students Tackle Multi-Step Assignments

            In this Edutopia article, consultant Sarah Kesty suggests a strategy for helping students break long-term assignments and projects into manageable chunks and avoid last-minute stress and missed deadlines:

            • Scan and plan – When a multi-step assignment is first introduced, the teacher explains to the class what it’s all about and helps students answer three key questions: 

-   Points – What counts and how much?

-   Product – What will I have created when I’m done?

-   Due date – What’s my deadline?

“Paradoxically,” says Kesty, “it’s in recognizing the demands of an assignment that many students experience clarity and relief. What seemed overwhelming (and thus something to avoid) becomes clear and less intimidating.”

            • Chunk it – The teacher helps students break the assignment into smaller pieces and think through an action sequence – for example, with a research paper:

-   Create a research question.

-   Look for articles.

-   Read the articles.

-   Annotate the reading, etc.

Students then plan backwards from the due date and create a calendar for each step, realizing that some take longer than others. “Many students like to add a little reward for hitting their personal project step deadlines,” says Kesty, “a habit-forming strategy that can boost the likelihood of completing a step or task.” 

            • Monitor and adjust – Reality often intrudes – for example, unrealistic pacing or sports practices taking evening time that was set aside for working on the assignment. A daily class check-in helps students make necessary adjustments so they can hit the final deadline. 

            “This method,” Kesty concludes, “empowers students to use strategies that support their independence and can be an effective way to help students decrease procrastination while practicing important executive functions.”

 

“How to Help Students Avoid Procrastinating” by Sarah Kesty in Edutopia, April 17, 2025

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6. Douglas Reeves on Getting Grading Reform Unstuck

            In this Creative Leadership Solutions article, Douglas Reeves says the shift to standards-based grading has run into trouble in many schools. “The failure of grading reform is often a self-inflicted wound,” he says, “with school systems falling victim to fads, unnecessary complexity, and silly controversies.” Reeves has six suggestions:

            • Focus on accuracy, transparency, and fairness. People may quarrel about the details, but most everyone agrees that grades should not depend on the “idiosyncratic opinions of the evaluator but rather on transparent criteria on which students are judged compared to an objective standard,” says Reeves. “This is how we evaluate pilots, drivers, and brain surgeons; it is the standard by which we should evaluate students.” 

            • Focus on consistency. Students in different classes who produce the same level of work on homework, quizzes, and tests should receive the same grade, he says. But in too many schools, “It is as if at every basketball game that students play, the height of the basket, the shape of the ball, and the number of players on the court are constantly changing.”

            • Keep it simple. Multi-page standards-based report cards using difficult-to-understand criteria are burdensome for teachers, convey the false impression that every standard has equal value, and turn off many parents. Mom and Dad want to know, How’s my kid doing? Grades need to be few, clear, and specific, communicating the level of mastery and pointing the way to improvement. And teachers, not computer algorithms, should be giving grades.

            • Don’t try to do it all at once. Grading reform has many possible components, and it’s best to start with one – for example, grading students on end-of-semester proficiency rather than averaging students’ assignments. This leads to significant reductions in failure rates, and will build momentum for further improvements in grading practices. 

            • Focus on performance. Getting an A should mean more than “extra credit, parental pressure, gamesmanship, and student negotiation,” says Reeves. “This turns students into mindless grade-grubbers and teachers into accountants.” The difference between an A and a B should be about the level of quality and rigor, not points on a 100-point scale. 

            • Avoid unnecessary battles. The distinction between using letters (A B C D F) or numbers (4 3 2 1) and the debates about re-takes and adopting a minimum grade of 50 are distractions, says Reeves. “The values of accuracy and fairness are far more important than the nomenclature of letters and numbers.” 

 

“Why Grading Reform Is Stuck” by Douglas Reeves, Creative Leadership Solutions, July 11, 2024

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7. Graphic Novels on Families

            In School Library Journal, Brigid Alverson recommends these graphic novels about the family dynamics of love, loss, and lineage:

-   Crumble by Meredith McClaren, illustrated by Andrea Bell, grade 3-6

-   Cassi and the House of Memories by Dean Stuart, grade 4-7

-   Soul Machine by Jordana Globerman, grade 7 and up

-   Low Orbit by Kazimir Lee, grade 8-12

-   Family Force V, Book 1 by Matt Braly, illustrated by Ainsworth Lin, grade 9-12

-   Bad Dream: A Dreamer Story by Nicole Maines, illustrated by Rye Hickman, gr. 9-12

-   Little Moons by Jen Storm, illustrated by Ryan Howe, grade 9 and up

 

“Family Ties” by Brigid Alverson in School Library Journal, May 2025 (Vol. 71, #5, pp. 34-37)

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