The implementation of the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) has the potential to move forward key features of standards-based reforms in mathematics that have been promoted in the United States for more than 2 decades (e.g., National Council of Teachers of Mathematics, 1989, 2000; National Science Foundation, 1996). We believe that this is an especially opportune time to purposely focus on improving the mathematics education of students who have historically been denied access to a high-quality and rigorous mathematics education in the United States, specifically low-income students and students of color (e.g., Kitchen, DePree, Celedón-Pattichis, & Brinkerhoff, 2007; Leonard & Martin, 2013). We discuss a challenge to realizing standards-based reforms in mathematics in the United States: computer-based interventions in mathematics classrooms.
Key words: Computer-assisted instruction; Diversity and equity; Standards-based reforms
This is an important time in the history of mathematics education in the United States. As of this writing, 43 of 50 states, the District of Columbia, four U.S. territories, and the Department of Defense Education Activity have adopted the Common Core State Standards (Common Core State Standards Initiative, 2015). We believe that the implementation of the Common Core State Standards for Mathematics (CCSSM; National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], 2010) has the potential to move forward key features of standards-based reforms in mathematics1 that have been promoted in the United States for more than 2 decades (e.g., National Council of Teachers of Mathematics [NCTM], 1989, 2000; National Science Foundation [NSF], 1996). In particular, we consider this to be an opportune time to purposefully focus on improving the mathematics education of low-income students and culturally or linguistically diverse students2 who have historically been denied access to a high-quality and rigorous mathematics education in the United States (e.g., Jacobsen, Mistele, & Sriraman, 2013; Kitchen, DePree, Celedón-Pattichis, & Brinkerhoff, 2007; Leonard & Martin, 2013; Téllez, Moschkovich, & Civil, 2011). In this Research Commentary, we argue that computer-assisted instruction (CAI) presents a challenge to realizing standards-based mathematics reforms for underserved students in the United States.3
During the 2009–2010 school year, more than 21 million students in the United States attended schools that received supplemental federal funding (i.e., Title I funding) to improve the academic achievement of children from low-income families (U.S. Department of Education, 2014). This was approximately 44% of all students in Kindergarten to Grade 12 (Hussar & Bailey, 2013). Although these are the most recent data available, the current figures are likely to be similar. In recent years, there has been an influx of federal dollars for educational interventions for Title I schools as part of the No Child Left Behind (NCLB) Act of 2001.4 The purpose of NCLB was “to ensure that all children have a fair, equal, and significant opportunity to obtain a high-quality education and reach, at a minimum, proficiency on challenging State academic achievement standards and state academic assessments” (U.S. Department of Education, 2004b, “Sec. 1001. Statement of Purpose,” para. 1). Technology should be employed by schools and school districts to ensure that students achieve academic proficiency (U.S. Department of Education, 2004a). From 2007 through 2014, an average of $14.1 billion of NCLB funding was devoted to Title I grants to low-performing school districts throughout the United States (New America, 2015).
Given the influx of federal dollars into Title I schools and the growing educational technology industry—investments in educational technology companies nationwide have tripled in the last decade, from $146 million to $429 million in 2011 (DeSantis, 2012)—we believe it is important to understand the impact that technology is having on mathematics instruction in Title I schools. A concern for us is that Title I schools disproportionately use educational technology such as CAI to “learn or practice basic skills” (Gray, Thomas, & Lewis, 2010, p. 3); 83% of students attending a Title I school experience technology primarily for skill development, compared to 61% of their counterparts at non-Title I schools (Gray et al., 2010). Because standards-based mathematics instruction may not be a priority at schools attended mainly by underserved students (Kitchen, 2003; Martin, 2013), we wonder what role CAI is playing with regard to the low-level, skills-based mathematics instruction that has been pervasive in these schools (Davis & Martin, 2008; Secada, 1995). More specifically, we pose the question: How may CAI support or hinder standards-based education reform in mathematics (e.g., development of students’ reasoning through problem solving and discourse), particularly in schools largely attended by underserved students?
For the purposes of this commentary, we adopt the commonly held perspective that CAI is an instructional approach in which a computer, rather than an instructor, provides self-paced instruction, tests, and learning feedback (Seo & Bryant, 2009).5 To be clear, it is not our intent to characterize CAI programs as uniform because large differences exist. For instance, programs vary in terms of interactivity, use of graphics, and versatility (Barrow, Markman, & Rouse, 2009). Some are software programs, whereas others are web-based. In addition, we recognize that there are at least three different applications of CAI in the classroom: supplemental, core, and computer-managed learning systems (Slavin, Lake, & Groff, 2009). The concerns we express here are intended to apply generally to any CAI intervention program designed for use in mathematics classrooms in U.S. schools, and some of these concerns may apply for some CAI programs and not for others. Our goal is to identify and discuss our apprehensions with regard to CAI in general and to attempt to explain why we believe our worries are particularly pertinent for underserved students.
To establish context, we give an overview of mathematical reasoning and discourse that are prominent in the CCSSM. We proceed to explore research about how underserved students are being denied access to a rigorous standards-based education in mathematics, provide some background on educational technology, and offer a brief review of the research on educational technology interventions that rely on CAI. We conclude with remarks about the need for more research to understand the influence of CAI on mathematics instruction at schools that serve students who have historically been marginalized by the U.S. educational system.
Mathematical Reasoning and Discourse
To implement standards-based reforms in mathematics, teachers need to possess a solid understanding of mathematics and have the pedagogical skills needed to support their students to learn mathematics with understanding (Franke & Kazemi, 2001; Hill, Rowan, & Ball, 2005). Reasoning is central to standards-based reforms in mathematics, specified among the five strands of mathematical proficiency presented in Adding It Up (Kilpatrick, Swafford, & Findell, 2001). For us, mathematical reasoning is synonymous with Blanton and Kaput’s (2005) definition of algebraic reasoning as “a process in which students generalize mathematical ideas from a set of particular instances, establish those generalizations through the discourse of argumentation, and express them in increasingly formal and age-appropriate ways” (p. 413).
A focal point of the CCSSM is the Standards for Mathematical Practice (NGA & CCSSO, 2010), which advocate for developing students’ abilities to reason mathematically across the K–12 curriculum. Among the eight practices, mathematical reasoning is prominent in three of them: Mathematical Practice 2, “Reason abstractly and quantitatively,” Mathematical Practice 3, “Construct viable arguments and critique the reasoning of others” (NGA & CCSSO, 2010, p. 6), and Mathematical Practice 8, “Look for and express regularity in repeated reasoning” (p. 8). Reasoning and proof were also significant process standards in mathematics education reform policy documents that foreshadowed the Standards for Mathematical Practice recommended in the CCSSM (e.g., NCTM, 1989, 2000; NSF, 1996).
Another prominent feature of the CCSSM is the value placed upon mathematical conversations or discourse. During mathematical discourse, the teacher seeks to foster and continually engage in dialogue with her students (Cazden, 2001; Herbel-Eisenmann & Cirillo, 2009). Research has demonstrated that when students have opportunities to engage in mathematical discourse to explain their ideas to peers and to listen to and make sense of the ideas of others, their learning is enhanced (e.g., Herbel-Eisenmann & Cirillo, 2009; Webb, 1991). As students engage in mathematical discourse through participation in learning communities, they build on their prior experiences and knowledge to achieve more advanced understanding of challenging mathematical concepts (Franke & Kazemi, 2001; Lave & Wenger, 1991; Stein, Silver, & Smith, 1998).
Mathematics Education for Low-Income Students and Students of Color
In 2013, the poverty rate was 14.5%, with 45.3 million people living in poverty in the United States (DeNavas-Walt & Proctor, 2014). Moreover, the poverty rate for ethnic and racial minorities in the United States in 2013 was much higher than the national poverty rate of 14.5% (DeNavas-Walt & Proctor, 2014). In 2013, 27.2% of Blacks and 23.5% of Hispanics were poor, compared to 9.6% of non-Hispanic Whites and 10.5% of Asians (DeNavas-Walt & Proctor, 2014). Also in 2013, the poverty rate for children under the age of 18 was 19.9% (DeNavas-Walt & Proctor, 2014), but it was 39% for Black children and 32% for Hispanic children (National Center for Education Statistics, 2015). Massey (2009) contended that advantages and disadvantages procured from an individual’s socioeconomic status (SES) are both reinforced and compounded by geographic concentration; Tate (2008) referred to this as the “geography of opportunity” (p. 397). Students from low-income communities attend schools in which pupil expenditures compare unfavorably to pupil expenditures in schools located in wealthy communities and achieve at lower levels than their wealthy counterparts (Payne & Biddle, 1999). For example, Hogrebe and Tate (2012) found that the SES of local communities is significantly related to students’ performance in algebra, with students from low-income communities achieving at lower levels than students from affluent communities. Brynes and Miller (2007) argued that SES not only has direct effects on mathematics achievement but also has indirect effects on both the opportunities students have to enroll in advanced mathematics classes in high school and on their propensity to take advantage of learning opportunities in mathematics.
In addition to poverty and SES, student access to a challenging standards-based mathematics education is influenced by race, ethnicity, and English-language proficiency (Diversity in Mathematics Education Center for Learning and Teaching [DiME], 2007; Gutiérrez, 2008; Martin, 2013). For instance, schools that enroll large numbers of African American students often have disproportionately high numbers of remedial mathematics classes in which instruction is focused on rote learning and strategies that are intended to help students be successful on standardized tests (Davis & Martin, 2008; Lattimore, 2005). In response to the NCLB Act of 2001 and the demands to increase test scores, Davis and Martin (2008) argued that the preponderance of skills-based instruction negatively “shape[s] the lives of poor African American students in more significant ways than middle-class or affluent students” (p. 18). In schools that serve large numbers of immigrant Latino or Latina students who speak with an accent, use English words incorrectly, or speak in Spanish as a means to express themselves, educators, peers, and community members may assume that they lack the capacity to perform well in mathematics (Gutiérrez, 2008; Moll & Ruiz, 2002; Moschkovich, 2007). Ability grouping or tracking is another widespread practice in the United States that has disproportionately hurt underserved students (Oakes, 2005; Secada, 1992). Tracking continues to “divide students by perceptions of ‘ability’ and communicate to students the idea that only some people—particularly White, middle class people—can be good at mathematics” (Boaler, 2011, p. 7).
Given the high percentage of students of color living in poverty in the United States and the extensive research base that demonstrates that low academic expectations and lower pupil expenditures have historically been the norm at schools attended by underserved students (e.g., DiME, 2007; Ferguson, 1998; Flores, 2008; Knapp & Woolverton, 1995; Payne & Biddle, 1999), it is not difficult to surmise that millions of students are being denied access to instruction in which mathematical reasoning and discourse are used to solve complex tasks (Davis & Martin, 2008; Kitchen, Burr, & Castellón, 2010; Téllez et al., 2011). Because standards-based mathematics instruction may not be a priority at schools attended primarily by underserved students (Kitchen, 2003; Martin, 2013) and because technology plays such a large role in student skill development in these schools (Gray et al., 2010), we worry about the role that CAI may play in exacerbating historical injustices in mathematics education for underserved students.
Some Background on Educational Technology and Research on CAI
The educational technology market is a big business. In a 2011 survey, the overall market value for prekindergarten to Grade 12 nonhardware educational technology was $7.5 billion (Software & Information Industry Association, 2011). Since 2011, federal funding for educational technology in K–12 schools has been integrated into other funding streams in order to make technology expenditures more efficient for schools (Pascopella, 2012). This makes it difficult to track how much of the 2013 Education Department budget of $69.8 billion (Office of Management and Budget, 2012) is actually spent on educational technology (Pascopella, 2012). As the market share of educational technology companies grows (Software & Information Industry Association, 2011) and billions of dollars go to Title I schools (New America, 2015), there is a need for research that explores the consequences of CAI implementation (Säljö, 2010), specifically in Title I schools.
Research has demonstrated that CAI has both strengths and weaknesses, but overall its effect on student achievement is inconclusive. Among the strengths, students are provided with immediate feedback on their performance, instruction is individualized, and the program maintains evaluative information concerning students’ progress (Kulik & Kulik, 1991; Lockard, Abrams, & Many, 1997). Hu et al. (2012) found that students who participated in an afterschool program in which they received tutoring via a CAI program performed significantly better on a standardized test than nonparticipating peer students and that these students’ mean scores were equivalent to or higher than (although the difference was not statistically significant) scores of students receiving afterschool tutoring from teachers. Additionally, Slavin and Lake (2008) found in their review of CAI programs designed for use with elementary school students that “CAI effects in math, although modest in median effect size, are important in light of the fact that in most studies CAI was used for only about 30 minutes three times a week or less” (p. 481). Summarizing their findings, Slavin and Lake (2008) wrote, “A number of studies showed substantial positive effects of using CAI strategies, especially for computation, across many types of programs” (p. 481).
In terms of weaknesses, studies have also shown that use of CAI does not affect student achievement in mathematics. For example, the What Works Clearinghouse reported that a popular CAI program had “‘no discernible effect’ on student achievement” (as cited in Cavanagh, 2008, p. 4). As part of the NCLB Act of 2001, Congress requested a $15 million study by the U.S. Department of Education to examine the effectiveness of 10 different mathematics and reading educational software technology products (Gabriel & Richtel, 2011). The report was released in 2007 and was compiled from data collected during the 2004–2005 and 2005–2006 school years. The findings indicated that “after one school year, differences in student test scores were not statistically significant between classrooms that were randomly assigned to use products and those that were randomly assigned not to use products” (Campuzano, Dynarski, Agondini, & Rall, 2009, p. xv). This report focused on technology products in mathematics and reading, and none of the mathematics technology effects were statistically significant. Moreover, Slavin, Lake, and Groff (2009) determined in their extensive review of CAI programs designed for use with middle school and high school students that the “effect sizes were very small” (p. 839).
Given the inconclusive and, at times, contradictory research concerning the effects of CAI on mathematics learning and achievement, we wonder why schools are investing significant financial resources and valuable classroom time in these educational technology products. A 2010 survey (U.S. Government Accountability Office, 2010) asked school leaders and district officials how they chose curricula, and 58% responded that they had never heard of or consulted the What Works Clearinghouse, an initiative of the U.S. Department of Education that reviews education research and publishes findings relevant to school leaders. Many experts believe that decisions to purchase are based on politics, personal preferences, and marketing; it is more a matter of slick public relations pitches rather than the effectiveness of the actual products that influence sales (Gabriel & Richtel, 2011).
Addressing Our Question and Considering Our Concern
We now return to the question: How may computer-based interventions support or hinder standards-based education reform in mathematics in the United States, particularly in schools largely attended by underserved students? In order to address this question, we discuss four areas of concern that we have regarding the impact of CAI on mathematics education: (a) the individualized nature of CAI, (b) the tendency to utilize CAI for drill and skill development rather than to promote mathematics reasoning through discourse, (c) the lack of preparation and training teachers need to appropriately implement CAI and the consequences of CAI implementation on teachers’ work, and (d) the potential to use CAI as a replacement for mathematics teachers.
Our first concern has to do with the individualized nature of CAI. Although a strength of computer-based training is that such interventions allow for instruction to be individualized (Kulik & Kulik, 1991; Lockard et al., 1997), this strength could also become a weakness if students consistently engage in mathematics alone. As a consequence of the individualized nature of CAI programs, students often work in isolation from peers while interventions are taking place. Teachers may have limited opportunities to understand how to use CAI programs (Snow, 2011) in ways that engage students in discourse with peers to collaboratively solve problems. If students have limited opportunities to engage in mathematical discourse with peers, they will also have limited opportunities to develop their mathematical reasoning and conceptual understanding (Franke & Kazemi, 2001; Stein et al., 1998). Interestingly, Slavin et al. (2009) concluded that CAI programs that support student interactions “have more promise” (p. 839) than those in which students interact with the technology alone. Given the potential challenges inherent in CAI to engage students in mathematical learning communities, research needs to be conducted to understand the type of assistance that teachers need in order to learn how to utilize CAI to support the development of their students’ mathematical reasoning skills through discourse. This research should be undertaken in schools with large numbers of underserved students in which the tendency is for teachers to expect less of students and to focus more on skills-based instruction (Davis & Martin, 2008; Flores, 2008; Kitchen et al., 2007).
A second concern is that CAI may be used more for drill and skill development than as a means to promote mathematical reasoning through discourse (Ganesh & Middleton, 2006; Snow, 2011). The research, though mixed and incomplete, suggests that CAI holds promise to support the development of students’ calculations and skills in mathematics (Slavin & Lake, 2008). Desperate to improve test scores, school leaders may be willing to pay the high costs associated with purchasing, maintaining, and utilizing CAI with the hope that the program will, at a minimum, support the development of students’ mathematical skills. Although this is understandable, we believe that it is also important to consider the potential ramifications of introducing CAI into a school. For instance, secondary teachers have the tendency to use computers primarily for mathematical drill and practice (e.g., Manoucherhri, 1999; Weiss, Banilower, McMahon, & Smith, 2001). This is particularly problematic in schools populated by underserved students, given the long history in the United States of focusing more on skills-based mathematics instruction in these schools (e.g., Kitchen et al., 2007; Lattimore, 2005).
Clearly, challenges exist regarding the use of technology and equity (Dunham & Hennessy, 2008), and we believe such challenges should be taken seriously by instructional leaders as they consider not only the benefits of introducing computer-based interventions in their schools but also the potential drawbacks. Specifically, we fear that the ongoing use of and potential overreliance on CAI, particularly at Title I schools, may privilege skills-based instructional formats in general over those that focus on developing students’ mathematical reasoning through discourse to the continued detriment of underserved students.
Our third concern pertains to teacher training and how CAI may affect teachers and their work. While serving as vice president of the Software & Information Industry Association, Karen Billings described how schools often do not properly deploy the products or train teachers to use them (Gabriel & Richtel, 2011). Teachers are not being properly trained on the appropriate uses of CAI (Ganesh & Middleton, 2006; Snow, 2011), specifically on ways to support standards-based mathematics instruction. This is particularly a problem in diverse schools situated in low-income communities precisely because these schools have historically struggled to offer a challenging mathematics program (Ganesh & Middleton, 2006). Researchers (e.g., Heid, 1997) have argued that technology has the potential to act as a catalyst to promote reforms in mathematics education. As we have previously asserted, more research is needed to understand the supports teachers need in order to use CAI for the development of their students’ mathematical reasoning skills through discourse. For instance, what types of coaching models (West & Cameron, 2013) may be most appropriate to support teachers in learning how to appropriately use technology to promote standards-based reforms in mathematics?
Finally, researchers have expressed apprehension that computers are increasingly being used as a replacement for teachers rather than in support of a rigorous mathematics education program (e.g., Steele, Johnson Palensky, Lynch, Lacy, & Duffy, 2002). Certainly it may be the case that administrators turn to computers when they experience shortages of qualified mathematics teachers. Nevertheless, we worry that CAI programs may unwittingly contribute to the deskilling of teachers because such programs, particularly when used exclusively as a school’s curriculum, may become the official mathematics curriculum (Apple, 2000). The deskilling of teachers combined with low student expectations contributes to and promulgates the historical trajectory of deprived mathematics pedagogy that has predominated in U.S. schools populated chiefly by underserved students (Flores, 2008; Kitchen et al., 2007; Tate, 1995). Frey, Faul, and Yankelov (2003) also found that although students value interventions such as CAI to help them learn course content, online and computer-based tools do not satisfy their desire to interact with each other and the instructor. We believe that it is especially important in schools largely attended by underserved students for students to have opportunities to collaborate with others, given the tendency in these schools to move toward controlled forms of instruction that limit students’ opportunities to work collaboratively and learn from each other (Davis & Martin, 2008; Kitchen et al., 2010; Lattimore, 2005).
Final Remarks
Mathematics is best learned when students have opportunities to engage in discourse in which mathematical ideas are generated, shared, investigated, debated, and validated as a means to develop students’ mathematical reasoning (Franke & Kazemi, 2001; Herbel-Eisenmann & Cirillo, 2009). The research literature has consistently documented that schools that predominantly serve low-income students and large populations of culturally or linguistically diverse students have taught mathematics in ways that do not align with rigorous standards-based mathematics instruction (e.g., Davis & Martin, 2008). A strength of CAI is that it supports skills-based instruction (Dunham & Hennessy, 2008; Gray et al., 2010; Manoucherhri, 1999), but this mode of instruction has failed students for years (Jacobsen et al., 2013; Leonard & Martin, 2013). Moreover, we question how well CAI interventions can promote standards-based instruction in mathematics for underserved students in which the development of students’ mathematical reasoning is paramount. We also worry that schools serving large populations of underserved students that invest heavily in CAI may devote less human capital to ensuring that their students are also engaging in challenging problem-solving activities.
The companies that have developed computer-based interventions, like so many other consultants and for-profit companies, have clearly been a beneficiary of the NCLB legislation and the federal dollars that continue to be provided for educational interventions in Title I schools. However, it is not clear from research that students who regularly use these interventions have benefitted to the same extent (Campuzano et al., 2009; Slavin et al., 2009). CAI programs align best with skills-based interventions that have been tried for many decades in schools that serve low-income, diverse communities in the United States, but these interventions have generally failed to produce positive results (Flores, 2008; Kitchen et al., 2007). Given that computer-based technologies and interventions that promise a positive impact on academic achievement are not supported by a solid research base (Säljö, 2010), more research needs to be done on how CAI best supports the learning of mathematics, particularly the rigorous mathematics promoted in the CCSSM and mathematical processes such as mathematical reasoning and discourse. We also need more research to understand how CAI programs are actually being used in diverse schools located in low-income communities as compared to schools in more affluent, White communities. Finally, we need to better understand how teachers should be trained to use CAI as a means to support standards-based reforms in mathematics.
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Authors
Richard Kitchen, Department of Teaching and Learning Sciences, University of Denver, 1999 E. Evans Ave., Denver, CO 80208; [email protected]
Sarabeth Berk, Imaginarium, Denver Public Schools, 1860 Lincoln St., Denver, CO 80203; [email protected]
Submitted April 21, 2014
Accepted January 27, 2015
We would like to acknowledge the helpful suggestions that Dr. Nicole Joseph, assistant professor at the University of Denver, made as a reviewer of a previous draft of this Research Commentary. We would also like to thank the anonymous reviewers of this commentary, who provided valuable suggestions as well.
Footnotes:
1 Standards-based reforms in mathematics refer to mathematics curriculum and instruction that promote the development of student reasoning through problem solving and discourse (e.g., National Council of Teachers of Mathematics, 1989, 2000; National Science Foundation, 1996). Although differences exist, for our purposes, we use “standards-based reforms in mathematics” in this commentary as being essentially synonymous with reforms promoted in the CCSSM.
2 We use “low-income students” to mean students who are classified as living in poverty in the United States (DeNavas-Walt & Proctor, 2014).
3 Throughout, we use “underserved students” to mean low-income students or culturally and linguistically diverse students. We use “computer-assisted instruction” throughout this commentary to mean computer-based interventions and computer-based training.
4 The No Child Left Behind Act (NCLB) was signed into law by President George W. Bush in January 2002. The NCLB law significantly increased the federal government’s role in holding schools responsible for the academic progress of their students. The law placed a special focus on ensuring that schools improve the performance of certain groups of students, such as poor and minority students. States did not have to comply with the new law, but if they did not, they risked losing federal Title I funds (Klein, 2015).
5 “Dynamic geometry software” (e.g., Jones, 2000) and video game interventions (e.g., Barab, Gresalfi, & Ingram-Goble, 2010) do not meet this definition of CAI.