Academic Exchange Quarterly Fall 2005 ISSN 1096-1453 Volume 9, Issue 3
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Integrating Mathematics and the Language Arts
Zambo, Associate Professor of Mathematics Education,
and Jo Cleland, Professor Emeritus of
Integrating language arts into mathematics instruction has been a highly recommended instructional strategy. This study investigated elementary school teachers’ (n=438) confidence in, frequency of use, and perceived usefulness of strategies for integrating language arts with mathematics. Results indicated that teachers in grades 5-6 were less likely to integrate language arts into mathematics instruction than teachers in grades K-2 and 3-4. They cited the lack of sufficient classroom time for the integration of language arts into an already overloaded mathematics curriculum.
As students move beyond mathematics computation and procedures, communication and reasoning become important avenues to the higher-order mathematical processes (Matthews & Rainer, 2001). Multiple relationships between language arts and mathematics are apparent in the process standards identified by the National Council of Teachers of Mathematics (1989, 2000) and include problem solving, reasoning, communication, connections, and representations. Problem solving and reasoning are enhanced by student-to-student and student-to-teacher discourse. Mathematics and language arts are both means of communicating and making connections to real-world contexts. Mathematics and language arts both utilize representations to organize and convey information.
Within the professional literature of mathematics education and language arts education, teachers are encouraged to use a variety of language-based techniques to enhance mathematics learning. Reading, writing, listening, speaking, viewing, and visually representing can all be incorporated into mathematics lessons (Kolstad, Briggs, & Whalen, 1996). Quality books in which mathematics concepts are embedded can be used to contextualize mathematical ideas, clarify vocabulary, and increase interest (Helton & Micklo, 1997; Manning, Manning, & Long, 1994; Mountain, 1993). Exploratory talk helps children articulate their reasoning processes as they utilize mathematics manipulatives (Schram & Rosaen, 1989). When children write out descriptions of their mathematical thinking processes, misperceptions become apparent (McIntosh, 1991), vocabulary grows (Nevin, 1992), and students’ progress in mathematical thinking is documented (Helton & Micklo, 1997). How often do teachers use these language techniques to enhance mathematics instruction?
Both mathematics and language are problem-solving processes employing symbol systems to represent ideas (Burton, 1992; Braunger & Hart-Landsberg, 1994). When a teacher specifically links conversational and mathematical languages, she is fostering personal and collective construction of meaning (Beane, 1993). Metaphors and analogies can be used to show parallels between disciplines, thereby clarifying mathematical terminology (Mountain, 1993; Whitin & Whitin, 1997). Story writing helps students articulate their understanding of concepts (Wolf & Gearhart, 1994). How confident are teachers in their ability to help students recognize these parallels in linguistic and mathematical thinking processes?
The literature is replete with suggestions for using specific organizers for particular tasks (Tarquin, P. & Walker, S., 1996). When teachers make a conscious effort to show how a common tool can be used in both a language arts and a mathematics context, learning opportunities are maximized (Perkins, 1988; Caine cited by Poole, 1997). Venn diagrams, webs, feature analysis charts, tables, graphs, even poetry frames transcend subject areas (Braselton & Decker, 1994). Do teachers perceive these teaching tools, which are common across mathematics and language arts instruction, as useful?
A major criticism of the movement toward integration is that “thematic units do not provide enough instruction for students to become proficient in math, reading and writing skills” (Brodzik, MacPhee, & Shanahan, 1996). When instruction is compartmentalized, critics claim that time devoted to integration limits coverage in each discipline and that the thinking processes for each domain become less rigorous (Pena, Brown-Adams, & Decker, 1999). The schedule can, however, be organized in an integrative manner without compromising the coverage of discipline-specific skills (Manning, Manning, & Long, 1994). Also, the unique contributions of each field become clearer when applied in genuine contexts. Braunger and Hart-Landsberg (1994) report high success with integrative learning in which the theme centers on a real-life problem that necessitates the learning and application of basic skills. Motivation and retention increase when students have the “need to know” skills in order to accomplish an authentic task (Lauritzen & Jaeger, 1994). What do teachers perceive as obstacles to integrating content areas?
Despite general support for integration, there are limited data about teachers' beliefs and practices regarding mathematics and language arts connections. This study was an effort to increase the body of knowledge on this topic.
This research incorporated a survey study design using a questionnaire containing both Likert-type and open-ended questions. In addition to the questionnaire data, taped interviews were used to collect additional data to validate and amplify the quantitative results.
This research focused on the overarching question: What is the current status of mathematics-language (M-L) integration in K-6 classrooms? The answer to this question was sought by attempting to answer the following questions: 1) How useful do teachers perceive strategies for the M-L connections to be? 2) How confident are teachers in their ability to use these strategies? 3) How frequently do teachers use instructional strategies for mathematics-language connections? 4) What obstacles prevent the integration of M-L?
Sampling and Data Collection
Forty schools were randomly selected from all the public elementary schools in one county in a southwestern state which includes a major metropolitan area. Principals at 27 of the selected schools agreed to participate. Questionnaires were mailed to and returned by a contact person designated by each school principal. Questionnaires were distributed only to teachers who delivered mathematics instruction. Participation was voluntary. The final page of the questionnaire asked teachers to also volunteer for interviews and observations. Structured interviews were conducted with 12 volunteers, four from each grade level grouping (K-2, 3-4, 5-6), from a random sample stratified by grade level group and high or low agreement with the best practices from the questionnaire. It was anticipated that interviewing teachers who indicated high agreement and teachers who expressed low agreement with the best practices might lead to the identification of factors that influence teachers’ levels of use based on perceived benefits and obstacles to integration.
The development of the self-administered questionnaire took place as follows. A questionnaire, containing both Likert-type and open-ended questions, was developed after a review of the literature identified best practices for four areas of interest: 1) language-based techniques to enhance mathematics instruction, 2) awareness of parallels between linguistic and mathematical thinking processes, 3) the use of common teaching tools for language and mathematics, and 4) strategies for organizing cross-curricular (language/mathematics) instruction.
Likert items were grouped into three sections about Frequency of Use, Useful for Instruction, and Confidence in Using, listed strategies. An addition group of Likert-items measured teacher agreement with statements about instruction.
The questionnaire was administered to a small number of teachers to identify potential problems with clarity, responses that were difficult to interpret, and so forth. Revisions were made based on the teachers’ responses.
Descriptive statistics were computed for all Likert-type items. Differences among grade level clusters (K-2, 3-4, 5-6) were determined through ANOVA. Open-ended items and transcribed interviews were analyzed for common responses and recurring themes. Data from classroom observations were used to further explain the findings from both quantitative and qualitative analyses.
Data were collected from 438 teachers and
analyzed by grade-level clusters K-2 (n=171, 95 percent females), 3-4 (n=134,
93 percent females), and 5-6 (n=133, 77 percent females). Forty-eight percent of the subjects had
earned master's degrees or higher. The
subjects had been teaching an average of 12 years and had been at their current
grade levels an average of 6 years. At
the K-2 and 3-4 levels, about 96 percent of the subjects taught in
self-contained classrooms; at the 5-6 level, 81 percent taught in
self-contained classrooms. The others were in situations in which their grade
level had chosen to departmentalize.
departmentalized situation, all teachers at a grade level teach their homeroom
language arts in the morning. In the
afternoon, the students rotate between teachers for mathematics, science, and
social studies. In those cases, one
teacher would be responsible for teach er all
the mathematics at that grade level. , . Teachers reported that about 51
percent of their instruction could be considered integrated. This averaged 14.6 hours of integrated
instruction across all content areas per week with 5.1 of those hours spent
integrating mathematics instruction.
Teachers at all grade levels were equally and highly supportive of M-L integration, in general, as is indicated by their levels of agreement with several statements. With 5 = Strongly Agree and 1 = Strongly Disagree, teachers most strongly agreed (means in parentheses) that talking (4.46) and writing (4.28) about mathematics increased student achievement and that the use of graphic organizers (4.30) and authentic tasks (4.31) helps students to see cross-curricular connections. Teachers at all grade levels also tended to agree that integration increases student learning (4.22). However, Analysis of Variance found a significant effect (p < .02) for grade level on responses to integration increasing motivation. As grade level increased, the belief that mathematics-language integration increases student motivation decreased with means for grades K-2 (4.15), grades 3-4 (4.04), and grades 5-6 (3.89).
Teachers were asked to rate the usefulness of specific strategies for integration from 5 to 1 with 5 = Very Useful and 1 =Not at All Useful. The highest-ranked strategies across all grade level groupings were connecting mathematics with everyday language (4.47), using authentic tasks (4.50), having students talk about their mathematical thinking (4.42), and using graphic organizers (4.37). Significant differences (p < .02) between grade level groups were found in the perceived usefulness of using literature with embedded mathematics with means for grades K-2 (4.34), grades 3-4 (4.15), and grades 5-6 (3.92), having students write about mathematics with means for grades K-2 (4.07), grades 3-4 (3.92), and grades 5-6 (3.83), and using metaphors and analogies with means for grades K-2 (4.10), grades 3-4 (3.96), and grades 5-6 (3.92). The perceived usefulness of these strategies decreased as grade level increased.
Teachers were asked to rate their own confidence in using specific strategies for integration on a five point scale with 5=Very Confident and 1=Not at All Confident. Teachers across grade levels were most confident in connecting mathematics with everyday language (4.11), using authentic tasks (4.10), having students talk about their mathematical thinking (4.10), and using graphic organizers (4.08). A significant difference (p< .02) in confidence level was found in using literature with embedded mathematics with means for grades K-2 (4.36), grades 3-4 (3.93), and grades 5-6 (3.83); as grade level increased confidence decreased.
Teachers were asked to indicate their frequency of use of the selected strategies on a five point scale with 5 = Very Often and 1= Not at all. Teachers across grade levels indicated that the most frequently used strategies were teaching through authentic tasks (4.08), having students talk about their mathematical thinking (3.72), and providing graphic organizers (3.94). Significant differences (p < .02) between grade level groups were found for two strategies: Students reading books with math with means for grades K-2 (3.53), grades 3-4 (2.97), and grades 5-6 (2.75); as grade level increased the use of this strategy decreased; and Teacher connecting math and language with means for grades K-2 (3.39), grades 3-4 (3.34), and grades 5-6 (3.14); as grade level increased the use of this strategy decreased.
Related to frequency of use, teachers responded to an open-ended question which asked them to describe how they integrated mathematics and language arts in their classrooms. At all grade levels, word problems were listed as a common reading activity. Many indicated that the story problems made real-world use of mathematics. There were limited references to reading environmental print. In the lower grades, teachers mentioned using calendars and recipes. In the upper grades occasional mention was made of activities involving newspapers, maps, and directions for making models.
Based on overall scores for the Likert-type items, teachers were categorized as being in high or low agreement with the concept of integration. Upper grade (4-6) teachers with high agreement indicated that they conduct projects that require reading and mathematics. Some described simulations (e.g., creating a class business). Those with lower agreement stated that they more often connected mathematics with social studies and science than with reading/English. Writing for real-world purposes was limited to a few upper-grade references to survey summaries and a letter-writing activity.
K-4 teachers mentioned real-life applications in general, but gave few specific examples. Among those they did list were cooking activities, calendar time, sorting, money, and measurement (e.g., during book-construction). Teachers of grades 5-6 were of two types. Some saw word problems as the sole source of real-life applications of mathematics skills. Those with higher integration scores engaged in thematic teaching with long-term projects, including simulations (e.g., stock market tracking, business enterprises) and actual planning and implementation of events (e.g., school sales). Some teachers, across grades, stated that they asked students to think of ways they used mathematics in their own lives. In some cases this was formalized, but in most it appeared to be an incidental function of instruction.
The most frequently listed writing connection was the use of journals in which children explained how they reached their answers. The second most common use of writing was having students generate their own word problems. In the lower grades teachers asked children to write their own math-related stories. This type of activity ebbed over the grades until it was virtually non-existent in middle school.
Many teachers at all levels indicated that they have children explain orally the processes they used to reach their answers. A few described students working in cooperative groups to investigate concepts or solve problems through collaboration and dialogue.
Use of graphic organizers was limited. The preponderance of examples specified graphing information. In the primary grades, most were charting either personal favorites or information from reading materials. In the upper grades more emphasis was placed on graphing survey data. Most graphic organizers mentioned were used to compare and contrast. The tools suggested appeared in this order of frequency: graphs, tables, charts, Venn diagrams, and webs. No graphic organizers were specified beyond those given as examples in the teacher survey itself.
There were significant differences in students reading books with mathematics, and teachers connecting mathematics and language. For those two strategies, frequency of use went down as grade level increased. On the open-ended question, K-2 teachers stated that they frequently use literature read-alouds, poems, songs, and finger plays to introduce mathematical concepts. The use of literature and related activities appeared to diminish progressively as students moved through the grades. A few upper-grade teachers used biographies of famous mathematicians and scientists. Vocabulary development was mentioned more by upper-grade than by lower-grade teachers. Descriptions indicated that, by and large, the teacher gave definitions and/or required mathematics terms as part of spelling; there appeared to be no student generation of definitions in “everyday language” based on concept investigations.
Teachers also responded to an open-ended question about obstacles to integration. The major obstacle stated was time. K-2 grade teachers emphasized time needed for planning and locating/preparing materials. Teachers of Grades 3-6 more frequently identified time limitations due to scheduling (e.g., departmentalization, and short instructional periods) and high demands on instructional time to cover curricular mandates and prepare students for tests.
Another frequently mentioned constraint was lack of resources. In the lower grades, those who had the highest overall integration means seldom mentioned this factor, while those with lower scores expressed need, especially for more books with math concepts embedded. Teachers in the upper grades more often stated that the mandated/available materials do not match an integration model. Some mentioned the lack of resources for Spanish-speaking children. A few mentioned the need for more resources for using technology.
The third most frequently identified factor was lack of teacher knowledge/skill.
Overall there was expressed need for staff development that would provide more strategies for integration. New teachers and those with low scores indicated that they would welcome workshops and resources to increase their instructional repertoires. Many with high ratings indicated that they are always open to/eager for more ideas as well. Some mentioned the need for assistance in working with Spanish-speaking children to build mathematical and language concepts simultaneously.
The fourth most-common comment was a perception that students lack the capacity to understand the abstractions required for integration; instead they need direct skill development (algorithms, computation). Some teachers stated that it is important for students to learn the basics before trying to “go beyond” to integration. Several even mentioned that students prefer a how-to rather than a critical thinking approach. In the words of a 5th grade teacher, “Students want to know how to do math, but resist true understanding of concepts. They want a mechanical method requiring little thought.”
Teachers tended to feel confident in their ability to integrate mathematics and language arts instruction and believed that the strategies targeted in the questionnaire were very useful for mathematics instruction. This was not surprising given the major attention paid to content integration in the literature over the past two decades. It might be expected that teachers who recognize the importance of integration and are confident in their ability to integrate, would integrate. The frequency of use responses, however, were lower than the confidence and usefulness responses indicating that teachers, on average, are not integrating as much as would be expected.
The major obstacle identified by teachers was time. Teachers of the lower grades indicated a lack of preparation time for organizing integrative activities. According to interviews, teachers believed that the most useful materials for instructional integration are teacher produced. This assumed reliance on teacher produced materials places a high demand on teacher time for preparation.
Teachers of the upper grades indicated a lack of instructional time for integrative activities in an already overloaded curriculum. Many of these teachers appeared to view integration as an addition to the current curriculum instead of an alternate instructional approach. On the other hand, teachers with high integration scores indicated that they were able to meet district and local academic requirements in an integrative manner. Those teachers tended to have a student-centered approach to instruction using cooperative learning, authentic projects, and real-world investigations.
Although many teachers are not using integration at the level that might be expected, they expressed interest in professional development opportunities to improve their knowledge of strategies for integration. Effective professional development should provide teachers with materials that could easily be adapted for use in their classrooms, thus reducing preparation time. It should also help teacher to understand how integration can be used to address the required curriculum more effectively, thus making more efficient use of their limited instructional time.
The ultimate goal of integration is to provide students with a curriculum that promotes achievement across content areas. By incorporating life-relevant experiences that require reasoning and communication in both mathematics and language arts, progress toward reaching that goal will be made.
This study investigated teachers’ beliefs and practices concerning the integration of language arts into mathematics, including the use of writing, speaking, and reading in mathematics. Teachers at all grade levels felt confident in using the strategies for integration and saw them as useful. However, use of the strategies, especially at the higher grade levels, was low. With the current emphasis on mathematics learning and the potential of language arts integration for helping children understand mathematics, teachers need to be supported in their use of content integration as an instructional strategy.
indicated that a lack of time prevented them from using integrated
instruction. Teachers at the K-2 and 3-4
levels lacked the time to prepare activities that integrate
arts and mathematics. Teachers at the
5-6 level indicated that they did not have time for integrative activities in
their mathematics instruction because of an already overloaded curriculum.
Teachers from the early grades need time to work together to produce activities that connect mathematics with the language arts. Extra planning time during the school year or professional development opportunities during the summer that provide instructional planning time would address this need.
The upper grades teachers need planning time, but they also need to be shown that the integration of mathematics and the language arts is not something that is added onto the curriculum as extra activities. It is a change in the way lessons are taught so as to enhance learning through writing, speaking, and reading. If teachers can learn how to integrate in the true sense of the word, their beliefs about the usefulness of content integration may be sufficient to motivate them to increase their frequency of use.
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