4hWith Every ReasonEssayDraft

Who sees why a child got it wrong?

Igor Barani

I saw it first in medicine

A doctor used to learn much of what mattered by examining the patient. You looked, listened, pressed and tested, and your hands found what the story left out. That habit was thinning before the pandemic. Medical interns in 2012 spent about 12 percent of their time with patients and about 40 percent at a computer¹. Abraham Verghese called the version of the patient who lives in the record the iPatient².

Then the pandemic moved the visit itself onto a screen. Telehealth went from 0.15 percent of private insurance claim lines in April 2019 to 13 percent a year later³. It has since settled near 5 percent⁴. What stayed is the work that is mostly talk. Mental health accounts for about 62 percent of telehealth patients⁵. The specialties that need hands went back to the office⁶.

Video does some things well. At Mayo Clinic, video diagnoses matched later in-person diagnoses 87 percent of the time overall and 96 percent in psychiatry. For ear disease, where the doctor needs an otoscope, they matched 65 percent of the time⁷. New neurology patients seen virtually, mostly by video, were 2.2 times as likely to need a second assessment⁸.

One more finding from medicine matters for schools. When children’s own primary-care practices used telemedicine, they prescribed antibiotics less often than in person, with the same adherence to guidelines⁹. Commercial direct-to-consumer services gave children antibiotics at 52 percent of visits for respiratory infections, against 31 percent in primary-care offices¹⁰. The screen did better when the child’s own practice was holding it.

Then my daughter's school used i-Ready

I paid little attention to screens in schools until my daughter started at a private school that used i-Ready, a math program from Curriculum Associates. By the company’s account it reaches about a third of American students¹¹. A child takes an adaptive test, which places her on a path of online lessons¹². Each lesson has a tutorial, guided practice and a quiz, with characters the program calls Study Buddies. Passing work earns credits, which buy games¹³. The company recommends 45 minutes per subject per week, with the child passing at least 70 percent of lessons¹⁴.

My daughter struggled with it. So did we, her parents, when we tried to follow how it was teaching. The explanations were turgid and verbose, and the method was hard to see through the words. The lessons ran on stories, and the stories were boring. When she did not pass, it seemed to us that the path sent her back through the same lesson, or the one before it.

The company calls its test adaptive and its lessons personalized^11,15. Its own documents describe what happens after a wrong turn. A wrong answer brings instructional feedback¹⁶. A student who fails a lesson can retake it. Repeated failures in one area raise an alert for the teacher. Once a student has not passed two lessons in a domain twice, instruction there “has been automatically turned off”^15,17. Nothing in the documents I found claims the program works out why the child got the answer wrong. It changes the level and the pace. To us, the teaching itself seemed to come one way.

A program that acts only on whether a child failed can offer her more of what already failed. To me it looked like a sales job. It did not serve my daughter.

The evidence on whether it works is thin, and most of it comes from the seller. Education research measures effects in standard deviations, the usual spread of test scores, and most effects are small fractions of one. The strongest positive results for i-Ready, about a quarter of a standard deviation on state tests, come from studies the company wrote or paid for^18,19. In one, a single lesson counted as using the program¹⁸. In another, the comparison group, who took only the i-Ready test, started well ahead and needed heavy statistical weighting¹⁹.

The one independent, peer-reviewed study was funded by the federal Institute of Education Sciences. It found about 0.04 standard deviations on the MAP Growth test, roughly two extra weeks of instruction, and its authors call the analysis descriptive rather than causal²⁰. A federal randomized trial that included i-Ready was ended in February 2025 without results^12,21. Across math technology, measured effects shrink as studies get more rigorous, from about 0.20 in quasi-experiments to 0.08 in randomized trials²². Even a co-author of the most favorable study said the evidence is “certainly not a sufficient evidence base to just blanket adopt i-Ready”¹¹.

To be fair, 0.04 is positive, and nothing shows the product harms children. It is a small gain for the classroom time the program costs.

What a wrong answer says

Children’s mistakes in arithmetic are rarely random. Many come from a rule the child believes. In one large collection of multi-column subtraction work, the five most common faulty rules accounted for 45 percent of all errors²³.

Go back to the 34. A teacher can see where it came from. In the ones column the child took 3 from 7, because 7 − 3 is a subtraction she knows and 3 − 7 is one she cannot do. In the tens column she took 2 from 5. Smaller from larger, in each column. Every digit has a reason. The rule is wrong.

Repeating the lesson may not reach that rule. The child can apply it again, faithfully, and fail again. What reaches it is a question about the ones column and a bundle of ten sticks opened on the table. A teacher who sees the 34 knows which lesson to give. A pass or fail score does not.

I should be careful here. The research does not show that software which diagnoses the faulty rule beats simple reteaching. In one small study, a tutor that diagnosed subtraction errors reduced them more, yet test scores did not rise significantly more than with a tutor that did not diagnose²⁴. What the research does show is where the diagnosis lives when educational technology works. ASSISTments, an online homework program, gave seventh graders in Maine immediate feedback and gave their teachers a report of the common wrong answers to go over in class. In a randomized trial, their standardized-test scores were 0.18 standard deviations higher, and 0.29 higher for students at or below the median²⁵. In Delhi, a program that paired 45 minutes of adaptive software with 45 minutes of small-group teaching gained 0.37 standard deviations on independent tests, though not on school exams²⁶. In each success the software worked beside a teacher. The federal practice guide for struggling students makes a related point about practice drills. It “does not recommend merely giving students timed worksheets or putting students on a computer-based program without supporting their learning”²⁷.

What changed in ten years, and what did not

It would be convenient to say the iPad arrived and the scores fell. The data do not allow it. On the national assessment, eighth-grade math peaked in 2013, at 284. It had slipped to 281 by 2019, then fell to 273 in 2022 and 272 in 2024²⁸. The slide began years before a device for every child became the norm. That happened in 2020 and 2021, when 84 percent of districts gave a device to every elementary student and 90 percent to every secondary student²⁹. A device for every child did not start the decline.

The pandemic then took eight points off eighth-grade math in three years, and remote school made the loss worse where children had least. In high-poverty districts that stayed remote, students lost just under 40 percent of a school year in math. In districts that stayed open, they lost about 15 percent³⁰. Remote learning still explains only part of the national fall, and researchers disagree on how large a part³¹.

Screens did not replace teachers either, if you count heads. Public schools added about 32,000 teachers between the 2018–19 and 2021–22 school years, while enrollment fell 2.6 percent³². The job lost standing. In 2024 teachers earned 26.9 percent less in weekly wages than comparable college graduates, a record gap³³. In 2025 about one teaching position in eight was empty or held by someone not fully certified, and 40 states reported shortages in math³⁴.

So the change I worry about is harder to count. Software took a share of class time, about 45 minutes a week in math by the vendor’s recommendation¹⁴. With it went some control over what a child is taught next. Parents and teachers describe a path whose order they cannot control, and one parent calls it a black box¹¹. No national data measure how much math time moved from teachers to screens. I can say only what I saw.

In the recovery, California districts that spent relief money on tutoring and summer school gained the most. Thomas Kane, who studies the recovery, put it plainly. “We can’t just ask teachers to talk faster”³⁵. What helped was more time with people.

The case for plain teaching

On several points the research is clear. In 2021 the federal What Works Clearinghouse rated all six of its recommendations for students who struggle in math as supported by strong evidence. They call for explicit, systematic instruction and precise mathematical language. They call for well-chosen objects and pictures, the number line, structured teaching of word problems, and brief timed practice once a concept is understood²⁷.

Worked examples, studied before solving problems alone, have a medium-sized effect across ages, about 0.48 standard deviations³⁶. Unassisted discovery does worse than explicit teaching (−0.38), while discovery with strong guidance beats other methods (+0.30)³⁷. Struggling with a problem before instruction helps older students, but the same body of studies favors instruction first in grades 2 to 5³⁸.

The reason underneath is working memory. A child can hold only a few new things at once, and everything else on the page takes a share. That is why plain materials usually beat rich ones. Bland manipulatives helped problem solving (0.80), while perceptually rich ones hurt it (−0.27), though the rich ones did better on transfer to new problems³⁹. Children given realistic paper money solved fewer money problems than children given plain black-and-white bills, and fewer than children given nothing at all⁴⁰.

Interesting but irrelevant additions, such as jokes, stories and decoration, lower learning by about a third of a standard deviation across 58 studies⁴¹. Psychologists call them seductive details, and the harm tends to be greater for learners with little prior knowledge or less working memory⁴². Kindergartners in a heavily decorated lab classroom were off task 38.6 percent of the time, against 28.4 percent in a bare one, and scored 42 percent on tests against 55. That study had only 24 children⁴³. No one has tested i-Ready’s characters or stories directly. They fit the definition of seductive detail, though, and young children have the least prior knowledge of anyone in the classroom.

Words and numbers grow up together

A child learns the language of mathematics at the same time as the mathematics, and each leans on the other. Chinese, Japanese and Korean name eleven “ten-one.” Children who speak them build numbers from tens and ones more readily than English speakers do⁴⁴. The head start is real, small and temporary. It faded once English-speaking children were shown ten-cubes, and it was gone by grades 3 and 4^45,46. English has its own trap, because “fourteen” says the ones before the ten. German says twenty-four as “four-and-twenty,” and German first graders’ errors with that reversal predicted weaker math in third grade⁴⁷.

For number skills, the words a child knows for mathematics seem to matter more than her general vocabulary. When preschoolers’ mathematical language and general language were measured together, only the mathematical language still predicted their number skills⁴⁸. Wordy problems cost children who are still learning English⁴⁹, and simplifying the wording helps only a little, about three percent on rewritten test items⁵⁰. Teaching the language of problems shows larger effects. At-risk first graders taught the structure of word problems along with the language that carries it scored 1.75 standard deviations above controls on word problems, against 1.08 for structure alone⁵¹. Keyword tricks, such as “altogether means add,” have no research behind them⁵².

Working memory is where language and mathematics meet. Across studies, language and math correlate at about 0.42, and working memory and intelligence account for more than half of that link⁵³. Word problems dressed in stories are more closely tied to working memory than problems stated purely in mathematics⁵⁴. A child who must hold a story, a cartoon and an unfamiliar word has less left for the arithmetic.

Why a new series

A teacher’s specialized knowledge of mathematics for teaching was the strongest teacher-level predictor of young children’s gains, while certification and years of experience were not⁵⁵. Yet training teachers in content has had little effect on student achievement in rigorous trials, and tutoring has had the most consistent effect, about 0.20⁵⁶. The knowledge matters, and it is hard to train. So the materials may have to carry more of it.

My daughter’s struggle is why I wrote a new series. I grew up with mathematics taught with simplicity and focus, and without distraction. I love that style, and I wanted her to have it. The series puts a reason beside every step, and its tagline is “Every answer, with a reason.” It draws on three traditions.

Vasily Davydov’s curriculum starts before numbers. Children compare lengths, areas and masses, write the relations with letters, and model them with strips and line segments. Number arrives later, as how many times a unit fits into a quantity⁵⁷. Andrei Kiselev’s textbooks, the standard Soviet texts for nearly two decades⁵⁸, followed his rule of “precision, simplicity, conciseness”⁵⁹. One reviewer wrote of the English edition of his geometry that nothing in it “may even occasionally distract from the subject”⁶⁰. Singapore’s curriculum moves from objects to pictures to symbols and draws word problems as bars^61,62. Berinderjeet Kaur, one of its leading teacher educators, advises teachers to introduce few models and to use them consistently⁶³.

The three share what I care about most. Each puts one idea in front of the child, says it precisely and leaves out everything else. Focus has correlational evidence of its own. High-performing countries plan far fewer topics in the early grades. In grades 1 to 3 they plan three, three and seven, against fourteen, fifteen and eighteen in a composite of American states⁶⁴.

In With Every Reason, a new word enters only after the child’s hands have done the thing it names. The child’s own words come first, and the precise word follows. “You said take away. It is also called subtract.” The words stay the same from book to book. No study has tested whether everyday or formal words should come first. The order is my judgment.

Davydov’s curriculum has been studied in single schools and design projects, with striking demonstrations and no randomized trial^57,65. Kiselev’s books have no comparative studies at all, and one historian argues his name became a legend for the good old days⁶⁶. Singapore leads the world on international tests, but its curriculum shows small effects when it travels without its teachers. A randomized trial of a US version in Nevada found 0.11 to 0.15 standard deviations, and trials of a Singapore-inspired program in England found 0.08^67,68. Singapore has recruited its teachers selectively, paid them during training and given them about 100 hours of professional development a year⁶². About 80 percent of its primary pupils were also in private tuition in 2016⁶⁹. Most of Singapore’s lead probably lies in its system, above all its teachers.

A simple book will not teach a child by itself. It can put the reasons on the page, in plain words and plain pictures, so that the adult beside the child has them. That makes the teacher’s job easier and the parent’s job possible. It is what I hope these books can do.

KeepThe screen sees wrong. A teacher sees why.

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