Enhancing Mathematical Understanding for English Language Learners 

Introduction

The pressures on all students are immense, yet consider the challenges faced by English language learners (ELLs) who must develop mathematical schemas through a language they have not fully mastered: English. This report investigates the instructional challenges encountered by Grade 3 students at Al Riyadh Charter School, which adheres to the Common Core standards. Here, all students have been identified as ELLs with notably low proficiency in English. This linguistic barrier impedes their ability to grasp abstract mathematical concepts, thus affecting their comprehension and performance on the Measures of Academic Progress (MAP) exams.   Additionally, the current instructional strategy—characterized by the use of PowerPoint presentations with high information density, a lack of linguistic support, and insufficient scaffolding strategies - does not align well with the learning styles of ELLs. This study outlines an action plan based on literature reviews to address these instructional challenges and explores the implementation and outcomes of these strategies. 

Methodology 

Direct classroom observations constitute the foundational method of this research methodology. Observations were systematically carried out in Grade 3 classrooms over four weeks, utilizing structured guides. These guides facilitated the evaluation of language use and visual aids in explaining abstract mathematical concepts and the instructional strategies employed to engage students effectively.

Literature Review

Over the past several decades, research in elementary education has consistently demonstrated a deficiency in systematic and explicit vocabulary instruction, significantly impacting ELLs (Roser, 1982; Scott, 2003).  The scaffolding techniques used in this study for teaching academic vocabulary are aligned with established research and include intensive instruction over several days using multimodal strategies - writing, listening, speaking - and focusing on a carefully selected set of words for in-depth instruction  (Carlo, 2004; Kieffer, 2010; Silverman, 2009).

Research conducted by Janette (1993) indicates that certain instructional methods are ineffective due to the excessive cognitive activity they require from students, which is driven by the way the information is presented rather than the complexity of the content.  Such conditions force students to divide their attention among multiple information sources,  potentially hindering schema acquisition necessary for problem-solving or learning concepts. Moreover, the fifth principle from Mayer’s (1997) study supports the cognitive theory of multimedia learning, which advocates for using fewer extraneous words and pictures to enhance conceptual development.  

Description of the Observed Issue

• Language Barriers: The linguistic complexity of the language used in MAP testing and instructional materials often surpasses the English language proficiency of students. This complexity hinders their understanding of mathematical concepts and causes confusion and a disconnection from the content taught. Furthermore, they must first decode the language before addressing the conceptual or mathematical challenges (De Avila 1984). This dual challenge significantly slows their academic progress relative to their native English-speaking peers.

• High Cognitive Load: PowerPoint presentations in mathematics lessons frequently include an overwhelming array of visual elements, contributing to extraneous cognitive load (Anita, 2013). These presentations often feature extensive text, images, numbers, and mathematical operational signs displayed simultaneously, which can overwhelm students' working memory and distract them from the main learning objectives. 

For instance, as depicted in Figures 1.1 and 1.2, a slide is divided into separate sections for problem-solving, success criteria, and descriptions of classroom activities. This format may impose an extraneous cognitive load on students who are forced to split their attention across multiple sources of information. Furthermore, the slide contains extensive text in various fonts and sizes, which can be particularly overwhelming for ELLs as they attempt to comprehend both the language and the word problems simultaneously. The cognitive overload from processing too much information leads to a significant decline in information retention and comprehension (Anita, 2013), posing an especially challenging situation for students who must navigate linguistic complexity,  mathematical terminology and concepts.

Action Plan Implemented and Results

• Language Scaffolding

This study employed clear and simplified language to enhance the comprehensibility of instructional content and facilitate information processing among ELLs. It identified certain mathematical terms —such as 'thousands' versus 'thousandths' and 'multiple' versus 'multiply'— that sound similar but represent distinct concepts, as potential sources of confusion. To address this, terms were enunciated clearly and simultaneously written on the board, providing visual support to complement auditory information. Additionally, to enhance the development of mathematical language skills, students were prompted to pronounce new terminology, initially through choral responses followed by individual articulations (Gladis, 2013; Diane, 2014). Visual aids, such as diagrams, charts, and images, were used to depict mathematical symbols such as '≤' and '1/2', with their verbal descriptions provided underneath. These materials enabled students to reference the symbols or mathematical terminology during classroom discussions or when encountering written word problems. As a result, students demonstrated increased participation and confidence in their tasks, exhibiting a strong grasp of the concepts and perseverance in problem-solving.

• Conceptual Framework: 

PowerPoint slides were systematically organized into clear, logical sections, each focused on a specific element of the subject matter (Figures 1.3. to 2.5). This structured organization helped learners to mentally categorize and efficiently process information in manageable amounts (Gladis, 2013). Complex sentences were rephrased into simpler, more concise forms, significantly reducing the cognitive load required to comprehend instructions or questions (Janette, 1993). Core concepts were emphasized in the PowerPoint slides, and supplementary information such as success criteria and problem-solving strategies (e.g., CUBES) were displayed on posters, aiding students in focusing on essential content without distractions, and achieving the learning objectives. Moreover,  the strategic simplification and emphasis on key content have significantly enhanced information retention without overwhelming them with linguistic complexity (Gladis, 2013).

• Consistent and Clear Design: 

A uniform layout and design template was used across all slides (Figures 1.3. to 1.8), creating a familiar visual environment that helped students easily identify specific types of information (e.g., definitions, questions) and minimize visual clutter (Mayer’s, 1997). Design elements such as font size, colour, and placement were deliberately chosen to highlight critical information. As illustrated in Figure 1.4, the main topics were emphasized using larger fonts or contrasting colours, distinguishing them from less crucial details. Additionally, visuals such as images, diagrams, and real-world examples were integrated, making abstract concepts more accessible and relatable.  This design strategy kept students engaged throughout the sessions and fostered a more inclusive and effective learning atmosphere. 

Conclusion 

In sum, the recommendations included in this report, which are supported by academic studies and direct classroom observations, are anticipated to promote conceptual development. By reducing cognitive load and providing language scaffolding, the school can better support its students in achieving academic success.

References

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