The Benefits of Applied Math

This week's article summary is Applied Math Education Can Make Americans More Numerically Literate, and it’s written by a college science professor who bemoans her students lack of mathematical confidence and reasoning skills.

It’s a follow-up to a recent summary on the importance of math in elementary school.

Her worries extend beyond her classroom: due to math illiteracy, many adults are ignorant about personal finances and blindly believe politicians and others who spout exaggerated statistics without providing any evidence.

She encourages elementary schools to do a better job teaching math, including real-life applications so kids can see the connections between math and real-life.

As mentioned in the earlier summary, Trinity is in the vanguard of enhanced math instruction in elementary school. Over the past number of years, we’ve all seen our students and teachers gain much more confidence and comfort in math.

Joe

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As American elementary schoolchildren head back to school, one subject just might be the most dreaded of all—mathematics. 

A distaste for arithmetic, calculations, and numbers in general starts young in America, where it's socially acceptable to claim to "hate math" or simply "be bad with numbers." 

By the time U.S. students hit middle school, our educational system has already failed them. American 15-year-olds score far below their peers from other countries in mathematical literacy. 

I will meet many of these students a few years later in my college classroom, where they will react with dismay at encountering calculus-based modeling in biology class, a subject which, in their prior experience, was virtually a math-free zone. While math is a key tool of modern biology—allowing us to predict how diseases spread or calculate the sustainability of our food supply—it's usually avoided in introductory classes, where it's viewed as "too complicated.” 

The American educational system is failing to prepare its citizens to face mathematical challenges with confidence.

This "math anxiety" has serious social and political consequences. 

In personal finance, Americans typically struggle to scale expenditures with income. 

More dangerously, innumerate people may become data-avoidant, assessing risk and quality of arguments based on "gut feelings" rather than numerical facts.

In contrast, math and statistics classes provide us with the logic frameworks we need to assess risk and link the magnitudes of cause and effect, making us better decision makers. There's still a role for experts and pundits, who help us make sense of a complex world. But as an American voting public, we should strive for better mathematical reasoning skills to supplement these expert analyses.

Educators have shown that it's possible to build strong math skills from Day 1 by investing more time on mathematical reasoning in our elementary school classrooms. 

And for those who remember math as boring or recall struggling to learn something wholly disconnected from daily life, there's a solution—applied math, which grounds math concepts in real-world examples.

These examples can start early. When our research team visits second-grade classrooms, we use "helpful" and "harmful" relationships between animals and humans to introduce number lines with positive and negative values. 

Similarly, elementary school educators have shown time and again that music lessons improve student math scores by introducing students to this note-based arithmetic. The same concepts apply for little girls curious about engineering and little boys helping parents measure ingredients in the kitchen.

Even after we've left the classroom, let's challenge ourselves to stop flinching away from numbers or blindly trusting (or mistrusting) those reciting them. When hearing a number or statistic, let's adopt a "stop and study" approach, asking what's being argued, by whom, using what rationale. 

Mathematical reasoning gives us a core, common set of facts that we can interpret together. By building math skills—in the classroom and in adulthood—we can be part of an American public that prides itself in mathematical exceptionalism, not mathematical avoidance.

 

Explicitly Teaching Reading Comprehension

This week's article summary is Reading Comprehension Loses Out in the Classroom, and it's a follow up to last week's summary.

When I taught middle school humanities (language arts and history/social), one of my principal academic objective was to get my students to form, substantiate, and express (orally and in writing) their opinions.

For most humanities teachers the vehicles used to accomplish the above goals are reading novels, short stories, textbooks, and primary sources. Usually teachers ask their students to complete their reading assignments at home, and then the classroom is used to assess, deepen, and expand their understanding of the material they read.

I always thought that through class discussions I could assess if my students were successfully comprehending their reading assignments. But, as you’ll see in the article below, I should have included more direct reading in my classroom.

Reading comprehension has remained an elusive goal in education. We know how important it is but struggle teaching and assessing it.

It’s critical to learn to decode words, develop an extensive vocabulary, and possess extensive background knowledge. Yet these skills don’t necessarily mean a student is effective at reading comprehension.

The article below recommends more direct reading in class – both by students themselves and from read alouds from their teachers. Thid should be followed from a class discussion of open-ended questions.

As I read the article, I kept thinking of two questions to repeatedly ask students about what they’re reading: What is the reading selection telling you? How do you know this?

Classroom reading is a staple of most elementary school teachers’ pedagogy. Yet, in addition to being entertaining for children, classroom reading is also a great opportunity to see if they are developing reading comprehension skills.

Joe

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Nearly a half century ago, a landmark study showed that teachers weren’t explicitly teaching reading comprehension. Once children learned how to read words, no one taught them how to make sense of the sentences and paragraphs. Some kids naturally got it. Some didn’t.

Since then, reading researchers have come up with many ideas to foster comprehension. Although the research on reading comprehension continues, there’s evidence for a collection of teaching approaches, from building vocabulary and background knowledge to leading classroom discussions and encouraging children to check for understanding as they read. 

This should mean substantial progress toward fixing a problem that was identified decades ago. But hardly any of these evidence-based practices have filtered into the classroom.

“It’s a little bit discouraging,” said Philip Capin of Harvard University’s Graduate School of Education. “What we often see in classrooms is devoid of high-quality strategy instruction or knowledge-building instruction.

Capin is referring to a host of comprehension strategies, such as checking yourself for understanding after reading a paragraph, identifying the author’s main point, or summarizing what you have just read.

Teachers spend limited time reading texts with children. The dearth of reading is especially pronounced in science classes where teachers tended to prefer PowerPoint slides over texts. More time is spent on reading comprehension instruction in reading or English class, but it was still just 23 percent of instructional time. Still, that is a big improvement over the original 1978 study, which documented that only 1 percent of instructional time was spent on reading comprehension.

A survey of middle school teachers published in 2021 echoes these observational findings that very little reading is taking place in classrooms. Seventy percent of science teachers said they spent less than 6 minutes on texts a day, or less than 30 minutes a week. Only 50 percent of social studies teachers said they spent more time reading in classrooms.

Capin said his team found that reading instruction was more focused on word reading skills, what educators call “decoding.” Researchers noticed that teachers were also building students’ knowledge, especially in science and social studies classes. But this knowledge building was mostly divorced from engaging students in text comprehension. 

Classroom researchers observed “low-level” reading instruction in which a teacher asks a question and students respond with a one-word answer. Teachers tended to confirm whether student responses were “right” or “wrong.” Capin said that only 18 percent of teacher responses elaborated on or developed students’ ideas. 

Capin said teachers tended to lecture rather than encourage students to talk about what they understand or think. Teachers often read the text aloud, asked a question and then answered the question themselves when students didn’t answer it correctly. He said that leading a discussion might help students better understand the text. 

Capin said teachers also often ask generic comprehension questions, such as “What is the main point?” without considering whether the questions are appropriate for the reading passage at hand. For example, in fiction, the author’s main point is not nearly as important as identifying the main characters and their goals.

Some teachers are leading reading discussions in their classrooms. Capin said he visited one such classroom a few weeks ago. But he thinks good comprehension instruction isn’t commonplace because it’s much harder than teaching foundational reading skills. Teachers have to fill in gaps in students’ skills and background knowledge so that everyone can engage. Teacher training programs don’t put enough emphasis on evidence-based methods, and researchers aren’t good at telling educators about these methods.

Interest in the science of reading has been exploding around the country over the past five years, especially since a podcast, “Sold a Story,” highlighted the need for more phonics instruction. Hopefully, we won’t have to wait another 50 years for comprehension to get better.

 

Rethinking Reading

This week's article summary is Rethinking Reading.

As you’ll see, more and more elementary schools are implementing Science of Reading curricula, e.g., Fundations, with their specific focus on strengthening word reading.

As we all know intuitively and through experience, strengthening student reading comprehension goes far beyond the ability to break down and read individual words. Quoting the article, ‘reading comprehension is one of the most complex activities, and our ability to do so is dependent upon a wide range of knowledge and skills.’

A recent research study from an earlier summary notes that ‘phonics is just one crucial piece of the reading puzzle—which must eventually be applied to authentic reading materials, such as books and short stories, as a regular part of the reading diet that involves more advanced skills like comprehension, prediction, vocabulary, and sustained attention.’

The five components of reading (phonological awareness, phonics, fluency, vocabulary, and text comprehension) can erroneously be considered and taught as independent skills rather than in an integrated fashion befitting the complexity and gamut of reading comprehension. 

I am thankful that under the guidance of Marsha Harris we have made available this school year more content-rich reading materials to support student development of content-specific vocabulary and knowledge, as word reading is but one aspect of being a strong reader.

Joe

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How can this be?” This was the response of principal Jane Avery when she saw her school’s most recent third-grade reading scores. Three years ago, she worked with her primary grade teachers to adopt and implement a new reading curriculum based on the “science of reading” with systematic and explicit instruction in phonics. Ms. Avery expected that the curriculum would lead to greatly improved scores on the state reading exam. She was shocked to see only a small improvement.

Ms. Avery is not alone in her expectations. Many others have seen the recent emphasis on the science of reading as the answer to America’s “reading crisis.”

Researchers have made significant progress in our understanding of how children learn to read, and this work is having an impact on classroom instruction. Much of the emphasis has been on developing word reading accuracy and fluency through explicit instruction in phonics. Word reading is critical to reading achievement, but reading involves much more than recognizing the words on the page. Students must also comprehend what they read. 

Research within the science of reading has investigated what is involved in comprehension and how children learn to understand what they read. Some of the findings from this research have been incorporated into educational practice, but not all that is known from research has been implemented in the classroom. 

Many educators view comprehension as a component of reading and one of the pillars of reading instruction. This view is an outgrowth of the report from the National Reading Panel (NRP) that separates reading into alphabetics, fluency, and comprehension. In the report, alphabetics was further divided into phonological awareness and phonics, and comprehension was divided into vocabulary and text comprehension. Over time, these components, along with fluency, became known as the big five or the five pillars of reading instruction. 

Today, much of reading instruction in the United States is guided by this component model of reading.

One limitation is that it can give the impression that the five components are independent and can be taught individually. In practice, the components are generally best taught together in an integrated fashion. That is, phonological awareness is best taught in the context of phonics, and vocabulary in the context of comprehending a text.

A more significant limitation is that including comprehension (and vocabulary) along with other components gives the impression that comprehension is skill based and similar in complexity and malleability to the other components. The model also implies that like phonics, comprehension can be explicitly taught, and once acquired, can be applied to all texts. 

In recent years there have been significant advancements in the science of how to teach and assess comprehension that are beginning to impact educational practices. At the forefront is the movement toward providing integrated comprehension and knowledge instruction within content-rich literacy curricula.

The focus on knowledge is important because of the critical role it plays in comprehension. Knowledge lays the foundation for building our understanding of text and provides an anchor for holding new information in memory. But despite the importance of knowledge, it has typically been neglected in comprehension instruction, which has focused primarily on teaching domain-general reading strategies and general vocabulary. 

Researchers who have recognized the importance of knowledge have begun to examine the effectiveness of content-rich literacy instruction in the classroom. Systematic reviews of this research show that content-rich literacy programs successfully increase vocabulary and content knowledge, as well as performance on standardized tests of reading comprehension.