Developing deep learning in students at risk: Enhancing understanding

The first catalyst for moving beyond mastery and failed reforms is to foster general thinking.

At a Glance

• Reforms intended to help at-risk students have not had the desired results.
• For many students, a root problem is a lack of a general sense understanding of how to solve problems.
• The Higher Order Thinking Skills (HOTS) project helped Title I students and learning-disabled students build a general sense of understanding by engaging them in regular thoughtful conversations around key thinking skills.
• Teachers can apply the lessons from HOTS by engaging in regular Socratic questioning with students.
• Math educators can similarly help students develop a sense of understanding of math concepts by combining discussion with software that enables them to apply the rules to create their own problems and see the resulting solutions.

A frequent problem teachers encounter when moving through the curriculum is that even when you get students to master Topic A in a subject, you are generally starting at ground zero when introducing the next topic. You need to once again combat apathy and lower skill levels, especially among at risk students who may not have had previous access to deep learning.

Deep learning is where students develop such an intense interest in Topic A that they not only succeed at a high level, but they also are ready to learn the subsequent topics and make connections across multiple areas of learning. My extensive research and experience have shown that students born into poverty have the same intellectual potential as other students and are capable of this kind of deep learning in multiple content areas (Pogrow, 2005). However, their potential never gets tapped despite the many cycles of well-intentioned educational policy.

The never-ending cycle

Indeed, education policy has been stuck in spinning cycles of reform for 50 years. Education chases equality of outcomes by cycling back and forth between reforms every decade or so.

The scientific approach to reading did not work previously, so let’s switch to whole language or balanced reading. That does not work, so now let’s try a science of reading approach — ignoring that this was not previously successful. Inequality in learning algebra led California to require that everyone learn it in eighth grade. Whoops, bad idea! Now let’s prohibit everyone from learning algebra in the eighth grade. Bad idea, so let’s . . . And on and on. None of these policies change outcomes very much or get us closer to academic equity.

The result of the cycle of reforms is that learning gaps have rewidened since 1988, and eighth- grade reading and math scores are lower in 2024 than they were in 2003 (NAEP, 2025).

Nor have “evidence-based” interventions been effective. My November 2023 Kappan article demonstrated that the majority of evidence-based practices, including those certified by the federal What Works Clearinghouse, are not effective, and the evidence researchers produced generally exaggerated actual effectiveness.

Why, then, do so many well-intentioned reforms fail? Of course, we know some of the problems — poor attendance, generational poverty, and racism. But these have, unfortunately, always existed, and efforts to address them directly have been disappointing. Why?

The fundamental problem with the efforts to increase equity to date is that there are deep-seated fundamental blockages that none of the reforms have addressed. Failure to address these blockages, which disproportionately affect students at risk, are why the cycles of reform have not been successful — regardless of whether they have been progressive or traditional, less structured or more structured.

Producing deep learning for at-risk students at scale requires that we change some fundamental paradigms. If we can reverse some of our professional biases to address the hidden blockages, we can enable at-risk students to succeed at high levels and thereby increase equity — and increase the effectiveness of other reforms.

An inadequate sense of understanding

The first, and most fundamental, blockage to deep learning is that while students who come from a high-poverty background have the same intellectual capacity as everyone else, they tend to have an inadequate understanding of abstractions. (I know this is a politically incorrect statement that on the surface sounds demeaning, overly generalized, and a deficit perspective — but please bear with me.)

When I say students have an inadequate sense of understanding, I mean that they do not understand how to systematically strategize, generalize, and synthesize information to solve a problem. They simply guess the answer. When they incorrectly decide that they are not smart. As a result, they get discouraged without ever developing a true understanding of what learning is. If students don’t know how to understand and generalize, no reform — in any content area — can be successful.

This is especially true after the third grade, when the curriculum starts to require more abstract and synthesized forms of learning. Indeed, we know how to improve learning and increase equity in grades K-2. The real equity crisis starts around grade three because the structured methods that are effective in the earlier grade are insufficient for the more sophisticated forms of learning students are expected to master going forward. Starting in third grade, the absence of a sense of understanding places a ceiling on the level of what students can achieve. This explains why, since the inception of Title I in 1965, gains at the earliest grade levels dissipate after third grade. For example, evidence shows that first grade students in Reading Recovery make large gains. However, by the third and fourth grades, students in that program were reading significantly below similar students who had not been in the program (May et al., 2023).

A sense of understanding, sometimes referred to as general thinking, is the missing link for enabling at-risk students to learn at their full potential past third grade. However, general thinking development has not been a major effort in any of the reform efforts to date. This is because content-area specialists prefer trying to develop thinking-in-content skills. Daniel Willingham’s (2007) summary of the research concluded that general thinking development was not effective. (It was fortunate that I did not know this “conclusive” research finding when I developed a successful general thinking development intervention for students with learning disabilities and in Title I programs.)

The bottom line is that students without a sense of understanding have not, and will not, succeed in content-based problem solving any more than they would if you taught the course in a foreign language they have not first learned. A sole emphasis on content-based problem solving can only increase disparities. Fortunately, schools can develop students’ understanding within their existing structures and finances.

Developing a sense of understanding

Traditionally, children have developed a sense of understanding at the dinner table or similar settings where adults pose questions every day and moderate their children’s responses. Through these conversations, children learn what it means to think. The more frequent and the more sophisticated such conversations are, the higher children’s instinct for understanding and abstract/generalizable thinking becomes. Such conversation appears to be essential for developing a sense of understanding and the instinct to generalize in Western logical forms of reasoning.

In one well-known study, Betty Hart and Todd Risley (1995) documented the shocking disparity between the amount and nature of conversation students were exposed to in homes with caring parents of different socioeconomic statuses. This disparity does not reflect a lack of care or of intellectual ability on the part of low-income families. But it does reflect the stresses of poverty that schools can overcome. If students do not get access to the amount of needed conversation to develop a sense of understanding in the home, it can be provided in schools. How do I know this?

I developed and directed the Higher Order Thinking Skills (HOTS) project, which used Title I funds to provide students after third grade with daily thoughtful conversations of supplemental drill. The program, which ran for more than 26 years, ultimately served close to half a million Title I students in more than 2,600 schools and 49 states. We discovered that the program was equally effective among students with learning disabilities (LD), as long as they had a verbal IQ over 80. HOTS students consistently did substantially better on standardized and state tests — twice the growth in reading and math and triple the growth in reading comprehension — than students who didn’t receive the supplemental drill (Pogrow, 2005).

The success of HOTS

The reason HOTS was more effective than prior general thinking development efforts was because it was far more intensive and focused on children born into poverty. Willingham’s research (2007) involved general thinking interventions conducted over a short span of time, usually less than seven days, and with highly advantaged students, including graduate students who already had a sense of understanding. In such instances, content-focused thinking is warranted. (This is a general lesson in why it’s important to know the context of research findings. I cannot tell you how many experts in thinking development told me that the findings that I reported in HOTS could not possibly be true because we “know” that general thinking does not work!)

As the HOTS program expanded to new contexts, we collected data to determine under what conditions the program was most effective (Pogrow, 2005) We found that 35 minutes a day for one to two years in groups of five to eight was sufficient to develop a sense of understanding in the majority of at-risk students.

HOTS combined Socratic dialogue around students’ efforts to solve computer games. Students had to read to figure out how to play the games and had to explain the strategies that they developed to succeed. The curriculum had teachers ask them questions that encouraged them to generalize about the relationships of ideas across the software environments.

Once teachers started to engage in thoughtful conversations with the students, they invariably reported being shocked at how little the students understood about the process of using ideas and information in a strategic sense. That changed for the better — slowly and surely.

As students gained experience in systematic conversation that required the consistent use of the four key thinking skills that underlie all learning: metacognition, inference from context, generalization, and synthesis thinking skills, they began to internalize a sense of understanding. The development of a sense of understanding in students was evident not only by the dramatic increase in reading comprehension, but also by increases in their willingness to engage verbally and the growing confidence and sophistication of their verbalization — supplemented by increases in GPAs and placement on honor rolls. Over a finite amount of time and with the patience of wonderful teachers, students who would initially not speak became highly verbal in class. These students were now poised for academic success.

The enhanced academic capability struck home when a science coordinator in an urban middle school who was trying to add problem-solving content to the curriculum complained that the only successful students were former HOTS students — and that there were not enough of them. She thought that they had been in an elementary school gifted program and did not realize that they had initially been the lowest-performing students. In other words, once students have a sense of understanding, they can succeed in problem solving across content areas.

The barriers in the system

There is a way to remove a key blockage that limits academic success for the majority of Title I and LD students. So, what’s the problem with implementing it? As already discussed, research has mistakenly concluded that general thinking development is not effective, and content specialists continually delude themselves into thinking that they finally know how to develop the content-based problem-solving skills of all students.

At the same time, the special education community continues to grow, requiring its own distinct pots of money. Yet, our large-scale experience was that the vast majority of LD students responded to the HOTS thinking development treatment in the same manner as the Title I students. This suggests that most students who are diagnosed as LD have the same fundamental learning blockage as Title I students — a limited sense of understanding. This also suggests that the tier system of identifying LD students based on their lack of response to conventional treatment is, in most cases, a miscarriage of social justice. This miscarriage is because most LD students’ failure to respond to a drill approach after third grade is NOT resulting from neurological or psychological impairment — but from schools providing the wrong treatment.

Providing the systematic conversations that developed the general thinking skills of Title I and (misdiagnosed) LD students would most likely lead to a major growth in the academic performance of at-risk students after third grade.

Applying the lessons from HOTs

And while the HOTS program no longer exists, schools have two options to apply the knowledge generated about how to develop a sense of understanding. The first is for someone to use the principles and the scientific knowledge generated from this program (Pogrow, 2005, 2009) to develop their own form of intervention. Given the superior technological tools available, it would be much easier today to develop such an intervention than it was decades ago.

The more feasible option would be to train all teachers in a school on how to incorporate questioning methods and Socratic probing that develop the four key thinking skills into their everyday instruction. The goal would be to get all teachers in a school to commit to asking one or two of these types of questions every day in the normal process of instruction. I do not have any data on how effective this would be, but in theory this accumulated exposure over three to five years should work.

I have developed a training workshop, lasting three to four hours, which I will be glad to share with school/district trainers seeking to build such classroom conversations in schools. The ideal would be to start at the early elementary level and then expand it to middle school in subsequent years.

Increasing understanding in math

The lessons from HOTS can also be used to increase the understanding of content-related concepts, specifically in math. Math educators tend to underestimate how abstract even the most basic concepts are for at-risk students. For example, we tried to get fifth grade students from low-income homes to understand what operation to use to solve a problem (e.g., +,-, x, or /). Despite all the instruction they had received over the years on identifying operations, and despite our best efforts, we could not make any progress.

Then we created a simple software program that enabled students to put in operations rules to generate number series. They entered an operation, the starting number, and the constant value for generating the next number in the sequence. As they began to see the consequences of their actions in constructing the sequence, they could hide the last number in the sequence and convert their work into a problem for others to solve. Students then formed teams to compete at solving each other’s problems and sharing their own problems that they felt could fool other teams. The experience of structuring their own problems enabled them to intuitively solve the other teams’ problems.

Of course, this is a simple example. Could giving students tools for creating problems and seeing the solution be used for more complex problems? We tried this on the most complex type of math problem, word problems. Solving math word problems requires synthesizing both language and math concepts — which is problematic if you are struggling with either, let alone both.

We created a simulated form of artificial intelligence (not easy 30 years ago!) and created a story about a space creature trapped inside the computer who knew math but was trying to learn English to escape. This element of fantasy was more authentic to the perspectives of middle schoolers than trying to pretend the math problems were relevant to students’ lives.

As students entered sentences into the computer to teach it the math sequence, the creature would sometimes be confused about the language choices. But when the sequence made sense, the creature would provide the step-by-step mathematical solution. The teacher, not being an expert in the mind of space creatures, would constantly act puzzled and ask students why they thought the creature was confused or ask students explain why they thought the creature solved the problem the way it did. In a week, the students had developed a deep understanding of how to solve a wide variety of word problems.

Instead of having the teacher explain rules repeatedly, this method allows students create their own problems and present a solution. The role of the teacher is not to formally instruct but get students to reflect.

The next step is to have a team competition where one group of students prepares problems for another team to solve. Invariably, each team tries to create ever more complicated problems. With sufficient experience, students begin to intuitively understand the underlying math principles. They have created their own mental model of how the mathematical system works.

While the software and curriculum, called Supermath, are no longer available, the methods and principles are explained in more detail in my 2004 Kappan article.

From conversation to deep learning

We can reduce a key learning blockage after third grade and produce deep learning in at-risk students by developing their sense of understanding through intensive, sophisticated conversation before exposing them to discipline specific problem solving. Such conversation does not require changing the curriculum, just how teachers talk with students for part of the day.

Once at-risk students have a sense of understanding, they spontaneously engage in deep learning and can benefit equally from other good reform ideas — while also enabling other reform ideas that were heretofore unsuccessful to become successful. Students at risk can then learn content as well as anyone else — providing they choose to do so. This leads to the second key learning blockage — boring curriculum and instruction — which will be the subject of my future article in the Summer 2026 issue of Kappan.

References

Hart, B. & Risley, T.R. (1995). Meaningful differences in the everyday experience of young American children. Paul H Brookes Publishing.

May, H., Blakeney, A., Shrestha, P., Mazal, M., & Kennedy, N. (2023). Long-term impacts of Reading Recovery through 3rd and 4th grade: A regression discontinuity study. Journal of Research on Educational Effectiveness, 17 (3), 433–458.

National Assessment of Educational Progress. (2025). U.S. Department of Education.

Pogrow, S. (2004). Supermath: An alternative approach to using technology to teach math. Phi Delta Kappan, 86 (4), 297-303.

Pogrow, S. (2005). HOTS revisited: A thinking development approach to reducing the learning gap after grade 3. Phi Delta Kappan, 87 (1), 64-75.

Pogrow, S. (2023). Avoid evidence-based practices and the What Works Clearinghouse — unless…Phi Delta Kappan, 105 (3), 42-48.

Willingham, D.T. (2007). Critical thinking: Why is it so hard to teach? American Educator 31 (2), 8-19.

---

This article appears in the Spring 2026 issue of Kappan, Vol. 107, No. 5-6, pp. 61-65.