• by Kristin Grayson, M.Ed., and Veronica Betancourt, M.A. • IDRA Newsletter • August 2008 • Veronica BetancourtDr Kristin Grayson

We’ve all heard about the fourth-grade slump in reading. Jeanne Chall first defined the fourth-grade reading slump in 1983 as the time when students fall behind in reading. The premise is that the slump in reading occurs because of the change in academic language required to read grade-level content texts. Starting around the fourth grade, reading shifts from “learning to read” to “reading to learn” with the inclusion of a more extensive vocabulary, a heavier content load and a need for more background knowledge (Chall and Jacobs, 2003).

Gerald Coles states that this type of reading requires students to be familiar with less common words, employ wider reading and have a deeper comprehension of the content material (Coles, 2007).

Noted second language linguist and researcher Jim Cummins further makes reference to the fourth-grade slump and English language learners in many of his articles. He spoke about it just last year in a speech at the California Teachers of English to Speakers of Other Languages conference in San Diego (Meteor, 2007).

But there is a comparable slump that occurs in math achievement. Achievement gaps in math increase as the grade level goes up. The National Center for Educational Statistics as cited by Freeman and Crawford finds that 82 percent of Hispanic students nationwide are below proficient in math in the fourth grade (2008).

For the state of Texas, an analysis of Texas Assessment of Knowledge and Skills scores for 2006 (Texas AEIS data) shows a steady decrease for all three major subgroups for White, African American, and Hispanic students beginning at the fourth grade and continuing through the ninth grade.

For English language learners, the Biennial Report to Congress on the Implementation of the Title III State Formula Grant Program; School Years 2004-2006, indicates that only one state showed that English language learners had met annual yearly progress (AYP) in mathematics. The report also found that achievement in reading and math for English language learners decreased as the grade level of the students increased (Zehr, 2008).

A Pew Research Center Report states that across the board English language learners are less likely to achieve in reading and math. In fact, achievement gaps are in the double digits in mathematics in the five states with the largest English language learner populations (Fry, 2007). Clearly, the achievement gap and math achievement is a matter of grave concern.

The Language of Math

Just like reading is related to academic language, math is reflective of a specific academic language. Math has two types of language, words and symbols. And although math might be considered a universal language, it can be difficult for any student to understand. Math has new terms, such as coefficient and tessellation, and common words that are used in a specific mathematical way, such as scale and change (Freeman and Crawford, 2008). Math uses terms that may be used in other subject areas with different meanings, such as table, slope and run. Additionally, there are multiple math terms that mean the same thing, such as slope, rate of change, rise/run and delta y over delta x.

The academic language of math includes the ability to read, write and engage in substantive academic conversations (Freeman and Crawford, 2008).

E. Etsy states: “Like other languages, mathematics has its own vocabulary, grammar (principles that govern the correct use of a language), syntax (the part of grammar that concerns rules of word order), synonyms, negations, conventions, abbreviations and sentence structure…It is a specialized language with its own concepts and symbols that must be learned. Even if you can do some math, you might not be able to read math. Learning to read math takes work.” (2007)

Student Engagement Affects Math Achievement

Math achievement is critical for all students. In fact, it is considered to be the strongest predictor for college success (Sciarra and Seirup, 2008).Thus, improving instruction and achievement in math for all students has been at the forefront of educational topics in recent years. The final report of the National Mathematics Advisory Panel has an array of recommendations for improving math achievement in U.S. schools, including strengthening teacher math preparation for elementary teachers (U.S. Department of Education, 2008). For instructional practices, the panel recommends a combination of “student centered” and “teacher directed” methods. Research also supports other instructional methods under specified circumstances.

One approach to addressing the drop in math achievement scores, especially as related to the fourth-reading slump, is to consider student engagement during math instruction. In a 2008 study of U.S. high school students, investigators conducted a two-way analysis of covariance to test for the interaction of race and three levels of engagement and the effect on math achievement (Sciarra and Seirup, 2008). Key findings showed that the overall combination of three types of engagement (behavioral, emotional and cognitive) was significantly related to math achievement for all racial groups. Emotional engagement was a more significant predictor for Hispanic students than for other groups. Student engagement and math achievement are related.

What is student engagement? What does it look like in the mathematics classroom? How can elementary teachers, especially, help students engage in the language and the content of mathematics?

The Sciarra and Seirup study describes three types of school engagement. Behavioral engagement has to do with effort and appropriate conduct. Emotional engagement concerns students’ feelings and a sense of belonging. Cognitive engagement relates to the student investment in learning, the belief in the importance of doing well in school and doing what it takes to go beyond the minimum requirements for completion of coursework (2008).

IDRA also has conducted an extensive review of the literature of student engagement and of English language learner engagement, in particular (Solís, 2008). IDRA has compiled a list of student engagement indicators that a teacher can use to observe students during class to help guide teacher decisions for strategy adjustment and implementation.

These student indicators cluster around four areas of evidence showing:

  • Students as part of a community;
  • Student use of academic language, student concentration and focus;
  • Student confidence in performance; and
  • Students as active and participatory.

Strategies that teachers can use to help students, especially English language learners, engage in the learning around these cluster areas include:

  • Making the classroom environment and learning context conducive for interaction;
  • Ensuring that lesson preparation, delivery and plans integrate language and content with a variety of interaction modes (small group, pairs, large group) while addressing language proficiency levels;
  • Building teacher-student relationships that promote trust and high expectations with a respect for student background, culture and native language;
  • Using a sheltered instruction approach that makes content comprehensible while systematically and purposefully improving English language proficiency and skills; and
  • Including active and interactive experiences that are structured, rigorous and accountable.

A Student Engagement Scenario

Following is an imaginary scenario to show application of observation for student engagement and teacher strategy adjustment:

Fourth grade students are completing a handout with math word problems involving multiplication and division. The teacher observes that at least half of the class is not engaged. Those students happen to be the ones who usually score poorly on classroom assessments. Some are daydreaming, some are fiddling with things in their desk, while other students are playing with their pencils and erasers and talking and laughing with other students around them. Students who are engaged are writing on the handout, mouthing numbers and gesturing procedures that they are mentally doing – in other words they are immersed in the task.

The teacher wants all students, especially struggling math students, to be engaged. She decides to take another approach the next day. Instead of having students individually work on handouts, she arranges the desks in pairs. Her initial presentation of the lesson is begun by asking students a question about a real-life situation where one might use the concept under study. A question that addresses multiplication might be, “How could you determine the amount of food to cook if you add six relatives coming to eat along with the six people already present in your household?” Students talk among themselves, and then the teacher presents the concept under study by using PowerPoint screens and real-life objects along with the mathematic numerical representation (visuals for comprehensibility).

She asks students to brainstorm words that she has used in the presentation that they might use in other situations or in other subject areas, such as the words times, table and order (systematic building of word knowledge). She asks students if any of the words are like words in their home language, pointing out words such as division and multiplication (awareness of cognates for language transfer).

Then the students work in pairs. She structures the work so that for each word problem only one student will see, read aloud and explain how to solve the problem to the other. The student is to use vocabulary words (academic mathematical language) that are specified by the teacher and posted in the front of the class. The other student is to record the solving of the problem according to the exact description by the first student (encourage both language comprehension and production skills). Discussion ensues among the pairs about the solution to the problem. Then the roles are reversed (encourage interaction), and another problem is read, explained and solution written.

In the final phase of instruction, pairs work together with another pair to compare their work and agree on a final solution to the problem (pairs to small group). The class, as a large group, then receives the final feedback from the teacher.

During the entire class period, the teacher is monitoring for student engagement and making adjustments to the process to maximize the engagement. At the end of the class period, the teacher briefly reflects and mentally notes strategies used that helped students engage conceptually and linguistically in mathematics.

Student engagement is one of the critical components of the IDRA Math Smart! professional development model. While there are other critical features to effective math instruction, the importance of student engagement in math achievement cannot be understated. Student engagement observation indicators can be the first step for a teacher to transform his or her approach to improving mathematics achievement starting at the elementary school level. This might be a paradigm shift for some teachers. The desired shift is to change the initial focus from, “What strategy should I use or try?” to “Are students engaged in learning with what I am already doing?”

If students are engaged, as evidenced by the indicators for student engagement, then the instruction can proceed with the approach being used. If students are not engaged or if assessment shows that students have not mastered the mathematical concept and language, the teacher can use the indicators to guide his or her choice of the next instructional strategy to implement.

Research is clear that increased engagement correlates with increased achievement in mathematics. By focusing on student engagement, teachers can help students improve in mathematics achievement.


Anthony, A. “Output Strategies for English-Language Learners: Theory to Practice,” The Reading Teacher (2008) 61, 472-482.

August, D., and T. Shanahan (eds.). Executive Summary: Developing Literacy in Second-Language Learners: Report of the National Literacy Panel on Language-Minority Children and Youth (Mahwah, N.J.: Lawrence Erlbaum Associates, 2006).

Chall, J.S., and V.A. Jacobs. “Poor Children’s Fourth-Grade Slump,” American Educator (Spring 2003).

Coles, G. “The 4th Grade Slump: What’s Wrong with the Brains of Slumping Children?,” District Administration (October 23, 2007).

Etsy, E. The Language of Mathematics (Published by author, professor at Montana State University, 2007).

Freeman, B., and L. Crawford. “Creating a Middle School Mathematics Curriculum for English-Language Learners,” Remedial and Special Education (2008) 29, pp. 9-19.

Fry, R. How Far Behind in Math and Reading are English Language Learners? (Washington, D.C.: Pew Hispanic Center, June 2007).

Meteor, B. “Jim Cummins Demolishes NCLB’s Ideology and Practice,” Daily Kos Newspaper (2007).

Sciarra, D., and H. Seirup. “The Multidimensionality of School Engagement and Math Achievement among Racial Groups,” Professional School Counseling (2008).

Solís, A. “Teaching for Cognitive Engagement – Materializing the Promise of Sheltered Instruction,” IDRA Newsletter (San Antonio, Texas: Intercultural Development Research Association, April 2008).

Texas Education Agency. Academic Excellence Indicator System, 2005-06 (Austin, Texas: Texas Education Agency, 2006).

U.S. Department of Education. The Final Report of the National Mathematics Advisory Panel (Washington, D.C.: U.S. Department of Education, 2008).

Zehr, M. “English-Learners Still Lag on Reading, Math Progress,” Education Week (April 2008).

Kristin Grayson, M.Ed., is an education associate in IDRA Field Services. Veronica Betancourt is an education associate in IDRA Field Services. Comments and questions may be directed to them via e-mail at feedback@idra.org.

The following article originally appeared in the August 2008 IDRA Newsletter by the Intercultural Development Research Association. Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]