Intervention based on science of reading and math boosts comprehension and word problem-solving skills

New research from the University of Kansas has found that an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.




The intervention, performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. This indicates that emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems. This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.



"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice.

For the research, trained tutors implemented the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem explaining that a person made a quesadilla for his friend Mario and gave him one-fourth of it, then asked students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas and what shape they were, and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator. The tutor explains that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario could impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key, as while ideally all students would begin on equal footing and there would be few variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition…. Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

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A mathematical bridge between the huge and the tiny

A mathematical link between two key equations—one that deals with the very big and the other, the very small—has been developed by a young mathematician in China.


The mathematical discipline known as differential geometry is concerned with the geometry of smooth shapes and spaces. With roots going back to antiquity, the field flourished in the early 20th century, enabling Einstein to develop his general theory of relativity and other physicists to develop quantum field theory and the Standard Model of particle physics.

Gao Chen, a 29-year-old mathematician at the University of Science and Technology of China in Hefei, specializes in a branch known as complex differential geometry. Its complexity is not in dealing with complicated structures, but rather because it is based on complex numbers—a system of numbers that extends everyday numbers by including the square root of -1.

This area appeals to Chen because of its connections with other fields. "Complex differential geometry lies at the intersection of analysis, algebra, and mathematical physics," he says. "Many tools can be used to study this area."

Chen has now found a new link between two important equations in the field: the Kähler–Einstein equation, which describes how mass causes curvature in space–time in general relativity, and the Hermitian–Yang–Mills equation, which underpins the Standard Model of particle physics.

Chen was inspired by his Ph.D. supervisor Xiuxiong Chen of New York's Stony Brook University, to take on the problem. "Finding solutions to the Hermitian–Yang–Mills and the Kähler–Einstein equations are considered the most important advances in complex differential geometry in previous decades," says Gao Chen. "My results provide a connection between these two key results."

"The Kähler –Einstein equation describes very large things, as large as the universe, whereas the Hermitian–Yang–Mills equation describes tiny things, as small as quantum phenomena," explains Gao Chen. "I've built a bridge between these two equations." Gao Chen notes that other bridges existed previously, but that he has found a new one.

"This bridge provides a new key, a new tool for theoretical research in this field," Gao Chen adds. His paper describing this bridge was published in the journal Inventiones mathematicae in 2021.

In particular, the finding could find use in string theory—the leading contender of theories that researchers are developing in their quest to unite quantum physics and relativity. "The deformed Hermitian–Yang–Mills equation that I studied plays an important role in the study of string theory," notes Gao Chen.

Gao Chen now has his eyes set on other important problems, including one of the seven Millennium Prize Problems. These are considered the most challenging in the field by mathematicians and carry a $1 million prize for a correct solution. "In the future, I hope to tackle a generalization of the Kähler–Einstein equation," he says. "I also hope to work on other Millennium Prize problems, including the Hodge conjecture."

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It’s common to ‘stream’ maths classes. But grouping students by ability can lead to ‘massive disadvantage

It is very common in Australian schools to “stream” students for subjects such as English, science and maths. This means students are grouped into different classes based on their previous academic attainment, or in some cases, just a perception of their level of ability.

Students can also be streamed as early as primary school. Yet there are no national or state policies on this. This means school principals are free to decide what will happen in their schools.

Why are students streamed in Australians schools? And is this a good idea? Our research on streaming maths classes shows we need to think much more carefully about this very common practice.

Why do schools stream?

At a maths teacher conference in Sydney in late 2023, I did a live survey about school approaches to streaming.

This survey was done via interactive software while I was giving a presentation. There were 338 responses from head teachers in maths in either high schools or schools that go all the way from Kindergarten to Year 12. Most of the teachers were from public schools.

In a sign of how widespread streaming is, 95% of head teachers said they streamed maths classes in their schools.

Respondents said one of the main reasons is to help high-achieving students and make sure they are appropriately challenged. 

But almost half the respondents said they believed all students were benefiting from this system.

We also heard how streaming is seen as a way to cope with the teacher shortage and specific lack of qualified maths teachers. These qualifications include skills in both maths and maths teaching.

More than half (65%) of respondents said streaming can “aid differentiation [and] support targeted student learning interventions”. In other words, streaming is a way to cope with different levels of ability in the classrooms and make the job of teaching a class more straightforward. 

The ‘glass ceiling effect’

But while many schools and teachers assume streaming is good for students, this is not what the research says.

Our 2020 study, on streaming was based on interviews with 85 students and 22 teachers from 11 government schools.

This found streaming creates a “glass ceiling effect” – in other words, students cannot progress out of the stream they are initially assigned to without significant remedial work to catch them up.

As one teacher told us, students in lower-ability classes were then placed at a “massive disadvantage”. This is because they can miss out on segments of the curriculum because the class may progress more slowly or is deliberately not taught certain sections deemed too complex.

Often students in our study were unaware of this missed content until Year 10 and thinking about their options for the final years of school and beyond. They may not be able to do higher-level maths in Year 11 and 12 because they are too far behind. As one teacher explained:

This comes as fewer students are completing advanced (calculus-based) maths.

If students do not study senior maths, they do not have the background for studying for engineering and other STEM careers, which we know are in very high demand.

On top of this, students may also be stigmatised as “low ability” in maths. While classes are not labelled as such, students are well aware of who is in the top classes and who is not. This can have an impact on students’ confidence about maths.

What does other research say?

International research has also found streaming students is inequitable.

As a 2018 UK study showed, students from disadvantaged backgrounds are more likely to be put in lower streamed classes.

A 2009 review of research studies found that not streaming students was better for low-ability student achievement and had no effect on average and high-ability student achievement.

What should we do instead?

Amid concerns about Australian students’ maths performance in national and international tests, schools need to stop assuming streaming is the best approach for students.

The research indicates it would be better if students were taught in mixed-ability classes – as long as teachers are supported and class sizes are small enough.

This means all students have the opportunity to be taught all of the curriculum, giving them the option of doing senior maths if they want to in Year 11 and Year 12.

It also means students are not stigmatised as “poor at maths” from a young age.

But to do so, teachers and schools must be given more teaching resources and support. And some of this support needs to begin in primary school, rather than waiting until high school to try and catch students up.

Students also need adequate career advice, so they are aware of how maths could help future careers and what they need to do to get there.

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