Calculators and Online Games: Supporting Students With Learning Disabilities in Mathematics

Abstract

With increased technology use in mathematics classrooms, as well as the increased prevalence of online instruction, digital calculators and online games are two types of digital tools that support students with learning disabilities (LD) in elementary and middle school mathematics. Teachers need to understand the advantages and limitations of different options and factors that help determine which tool may be most beneficial to support the goals of the mathematics lesson as well as the individual needs of students with LD. When used appropriately and efficiently, digital mathematics tools, such as calculators and online games, can increase students’ conceptual understanding of mathematics content as well as their confidence and engagement in the mathematics classroom. This column presents a variety of virtual calculators and online math games, why they are effective, how they can be implemented, as well as a short scenario depicting one way the tool can be used in the classroom.

Keywords

mathematics disabilities technology instruction

Technology is an important part of the teaching and learning of mathematics for all students and is endorsed by the National Council of Teachers of Mathematics (NCTM; Boyle & Kennedy, 2019; NCTM, 2015). Technology is embedded throughout mathematics education, including low-tech (i.e., devices that do not require power, such as concrete manipulatives), mid-tech (i.e., battery operated devices, such as calculators), and high-tech (i.e., generally computer-based, such as apps and smartboards) options (Chambers, 2020). Beyond supporting all students, technology can effectively support students with learning disabilities (LD) in accessing math education as well as increasing engagement (Boyle & Kennedy, 2019; Ok et al., 2019).

Students identified with an LD show consistent low achievement in mathematics over time despite displaying average intelligence (McDonald & Berg, 2018). In the math classroom, students identified with an LD in mathematics often struggle with the retrieval of basic math facts, creating mental representations of math concepts, number sense, and working memory (McDonald & Berg, 2018; Nelson & Powell, 2017). Similarly, students who struggle to make mental representations and struggle with number sense have a difficult time with the conceptual understanding of new math concepts (Nelson & Powell, 2017; Watson & Gable, 2013). Students who struggle in mathematics, such as students with LD, will continue to experience these struggles throughout later grades as well as in future employment opportunities (Nelson & Powell, 2017; Watson & Gable, 2013).

For students with LD who struggle in mathematics, technology can support the unique struggles students exhibit (Boyle & Kennedy, 2019). The use of instructional technology in mathematics is considered a high-leverage practice and the NCTM includes technology use as one of the six main principles, which should guide mathematics instruction (McLeskey et al., 2017; NCTM, 2000). However, technology is only effective if it is selected intentionally and based on what, why, how, and under what conditions the technology can be used (Thomas et al., 2019). Although a range of technology exists to support students, including students with LD in mathematics, this column focuses on two types of digital math tools: calculators and games. This decision does not diminish the value of other digital tools (e.g., virtual manipulatives, video-based instruction) but rather emphasizes the increased use of these two digital tools in Grades K–12 math classrooms, and the recent attention to digital supports for mathematics as a result of the Covid-19 pandemic (Kennedy & Boyle, 2021). This column presents what, why, and how for both tools, as well as scenarios depicting use in elementary and middle school mathematics.

Digital Calculator Tools

What

Calculators are one of the most common tools used in mathematics teaching and learning (Ellington, 2003; Lai & Berkeley, 2012). Historically, calculators have been a common accommodation provided to students with LD (Lai & Berkeley, 2012). While traditionally one pictures a calculator as a handheld tool, smartphones and tablets have changed people’s perception of and access to calculators. As ubiquitous as calculator apps are on mobile devices and computers, there are specific apps and web-based calculator options that can support students in the mathematics classroom and at home. See Table 1 for examples of digital calculator tools. These include digital tools that closely resemble handheld four-function or graphing calculators as well as options that allow students to write on an app or take a photo of a computational task to solve or prompt students with the steps of how to solve a problem (e.g., Cymath and Photomath).

Table 1.

Examples of Digital Calculators to Support Students with Learning Disabilities in Mathematics.

Digital calculators	Description	Why teachers might use with students
Photomath	App that allows users to take a photo of a written or printed problem and see multiple ways to solve the problem with step-by-step explanation for how to solve the problem. The app allows users to choose between 33 languages contains a help center and tutorials to show users the features of the app. The app also contains a history page to go back to previous problems users have solved for future reference. https://photomath.app/en/	• Photo option can support students who struggle with writing and typing. • Offers a variety of textbook problem solutions aligned to curriculum so students can check their homework. • Shows and explains steps to solve so students can see where they made their mistake and how to fix it. • Free • Can be used on any smartphone or tablet
Cymath—Math problem solver	A digital calculator that allows students to write on a virtual whiteboard (only on app version) or type equations into the app. The calculator shows step-by-step directions as well as explanations and the answer. Includes answers to basic operation, fraction, pre-algebra, algebra, and calculus problems. Website includes practice problems with hidden accompanying solutions and explanations across all listed mathematics topics. https://www.cymath.com/	• Allows students to take a photo or type problems using a keyboard. • Shows steps to solution to allow students to compare their answer and each step of solving the problem. • Premium option provides solution explanations for additional feedback for students. • Free with premium version available. • Can be used on any device with internet access.
ClassCalc	Online scientific, graphing, and matrix calculator. Teachers can create a class and share the class with students via class code. Teachers can enable test mode where students are locked on the graphing calculator for the duration of the test. Students type equations into the calculator using the keyboard and graph on the webpage. Students can zoom in and out and change axis lengths https://classcalc.com/graphing-calculator	• Includes basic, scientific, graphing, and matrix calculators so this option can be used in most Grades K–12 classrooms • Classroom mode allows teachers to see all students calculator screens so they can provide feedback to students in the moment • Lockdown option to keep students on task during assignments and tests • Free • Can be used on any device with Internet access

Why

Calculator use is supported by older research that suggests the benefits to students with disabilities and their typical peers, without negative effects (Burrill et al., 2002). Burrill et al. (2002) found students with access to and familiarity with graphing calculators not only received higher grades but also demonstrated greater conceptual understanding of the target mathematics as well as familiarity with additional strategies not observed in students without access to calculator instruction. Bouck et al. (2015) suggested simply providing a calculator to students without instruction was not effective, which contradicts the opinion calculators give students an unfair advantage. Calculators support students who struggle with processing or basic facts while still allowing them to practice more advanced mathematics skills (Bouck et al., 2015).

How

Teaching students how to use each of the calculator tools supports students in making informed decisions as well as the generalized use of the technology in the classroom (Bouck et al., 2015). To implement digital calculators and calculator apps or online tools (see Table 1 for examples), teachers first need to determine whether the calculator will exist as an accommodation for individual students or as a class-wide support. Teachers can make digital calculator apps accessible to students in the class and teach students the self-determination skills necessary to make decisions for when they need to use the tools, such as solving problems or checking answers (CAST, 2018). As Bouck et al. (2015) found, students need instruction to use calculators effectively, teachers should plan instruction on calculator use prior to providing calculators for student use. Instruction on calculator use should depend on the calculator selected (e.g., four-function, graphing, app) as well as the instructional goals. To teach students how to use a calculator, educators can utilize evidence-based practices such as explicit instruction or task analysis before providing students with the calculator. See the first scenario for an example of a task analysis for calculators and see the second scenario for a detailed discussion of explicit instruction. Doabler and Fien (2013) provided an in-depth discussion of explicit instruction in mathematics and McConomy et al. (2021) did likewise for support on task analyses.

Scenario

An eighth-grade student has a LD in reading and math, and experiences math anxiety¹. He attends math in the general education classroom where lessons are currently focused on linear algebra. In addition, he receives 1 hr of resource room support a day. He feels anxiety with learning algebra and likes to receive a lot of feedback from this teacher as he is completing his work. His resource room teacher feels like he conceptually understands how to solve the two-step linear algebra problems but needs a lot of reassurance. Given that he has his own phone, his special education and general education teachers encourage him and his family to install the Photomath app. In a joint meeting, his teachers teach him to use this tool to check his work after he completes each problem, clarifying this should not be used to just tell him the answer. His teachers use a task analysis to teach the steps required to use the Photomath app:

Write 2 × -4 = 8 on paper.

Solve the problem the best you can on your paper.

Open the PhotoMath app on phone or tablet.

Move camera over paper to align 2 × -4 = 8 in the red rectangle on the screen.

Press red button at the bottom to take photo.

Wait for app to solve the problem and provide the answer.

Compare your answer to the answer on the app.

If answers match, you have gotten the correct answer. Proceed to Step 14.

If incorrect, choose red button labeled “show solving steps.”

Expand each step by clicking on each of the down arrows on the right side of the screen.

Locate the step in which you made a mistake.

Read or listen to the explanation given.

Correct mistakes in problem on your paper.

Choose “x” in the top right corner.

Continue on to the next problem.

To use the app, following the task analysis, the student writes a problem and then writes the steps he uses to solve. When he is done, he scans the problem with the Photomath app and compares his answer and steps to the steps and answer on the app. When the steps or answers do not match, he can use the “explain steps” feature on the app to help him see where he made an error. This is helpful as it allows him greater independence. He can locate the step where he made an error and correct the error on his own. This decreases the feedback he needs from his teacher as he is receiving reassurance from checking his steps and answers with the app.

Online Games

What

Games are activities frequently implemented at home for fun. However, traditional as well as targeted math games can work to support students with LD in classrooms and at home in mathematics (National Center on Intensive Intervention [NCII], 2016). Although games were traditionally physical, such as with boards (e.g., Sorry), cards (e.g., Skipbo), dice (e.g., Yahtzee), or even paper and pencil (e.g., bingo), new online games relative to mathematics have begun to gain attention. While many for-purchase digital math games exist, such as Prodigy or IXL, there are also games connected to math curriculum, such as Investigations, Everyday Math, or CMP. See Table 2 for examples of online math games. Many of the curriculum-based mathematics games support understanding as well as fluency in mathematics and serve as an alternative to paper or digital worksheets or flashcards (Bay-Williams & SanGiovanni, 2021).

Table 2.

Examples of Online Games to Support Students With Learning Disabilities in Mathematics.

Online games	Description	Why teachers might use with students
Investigations	Library of mathematics games associated with the Investigations curriculum for students in Grades K–5 (Technical Education Research Centers, 2016). Games are aligned to curriculum, sorted by grade and content, and offer a variety of games across many mathematics topics. Each game includes simply stated rules and guidelines, and some allow for two or more players. Some games include print outs of directions, gameboards, and materials for playing face to face. https://media.pk12ls.com/curriculum/math/Investigations3/gamecenter/english/index.html	• Supports students with K–5 math skills; aligned to grade level standards and curriculum • Opportunity for students to play games in pairs More than 130 games available • Additional printable directions, game boards, and score cards for most games. • Free • Can be used on any device with internet access
Illuminations	Library of online mathematics activities including mathematics games from NCTM for Grades Pre-K–12. Games and activities are listed together but can be searched for by name or filtered by content standards (NCTM standards or Common Core) and grade level. Some have an option to play against a “computer” player. This supports individual students to play. https://illuminations.nctm.org/allgames.aspx	• Students can play with others or against the computer, which allows them to play at home • Aligned to NCTM and Common Core State Standards • Offers online activities and games • Grades Pre-K–12 • Free • Can be used on any device with internet access
CMP Games	Library of online mathematics games and activities for students in Grades 6 to 8, sorted by grade level content from the CMP curriculum (Lappan et al., 2014). Games are engaging and include little distraction. Each game and activity has detailed instructions on how to play the game and use the platform. Some games have options to play against a “computer” player good for individual student play. https://media.pk12ls.com/curriculum/math/cmp3/activities/index.html	• Aligned to CMP curriculum • Offers online and physical versions of the game; printable directions and game boards • Offers teacher and family resources to accompany games • Free • Can be used on any device with internet access

Note. NCTM = National Council of Teachers of Mathematics; CMP = connected mathematics project.

Why

As stated earlier, students with LD in mathematics struggle with recall of basic math facts and with fluency of mathematics skills, which can negatively impact students when learning new math concepts that build upon previously learned skills (Nelson & Powell, 2017). According to Mellott & Ardoin (2019), mathematics fluency is developed through activities that include frequent repeated practice, frequent reinforcement for accurate answers, and immediate feedback. Instead of the traditional methods to support fluency development (e.g., timed tests, mad minute worksheets), the NCTM (Rutherford, 2015) and the NCII (2016) endorse the use of instructional mathematics games to support the development of fluency in mathematics. Math games incorporate frequent opportunities to respond, embedded reinforcement, as well as frequent and immediate feedback from other players or supervisors. This supports the notion that mathematics games can be an effective way to practice fluency of mastered content in the classroom and at home. Moyer-Packenham et al. (2019) found students who played math games not only improved their mathematics language but also improved their ability to form representations and make connections among mathematics content. With the increase in students learning online, virtual math games can be an effective and efficient alternative to physical games for students learning from home.

How

Online math games can be used in a variety of ways inside and outside the mathematics classrooms. While there are many options for math games, it is important for teachers to select those that are appropriate for their students in terms of content, strengths, and skills (Moyer-Packenham et al., 2019). Games should include effective instructional strategies and should be designed for students with LD or be easily adaptable to support students in mathematics (Marino et al., 2011; Ok et al., 2016). Furthermore, it is important for teachers to consider and evaluate if the games they are choosing to implement into their classroom instruction have an effective design that includes ease of navigation, customizable settings, and an engaging background that is not too distractable (Marino et al., 2011). See Ok et al. (2016) for a rubric used to evaluate instructional apps for students with LD.

After students have acquired the content, teachers can incorporate math games as part of small groups in centers during work and free time as well as provide links to the game for students to play at home. Some online games even have the additional benefit of not requiring another person to play with the student (i.e., online games often have an online opponent or “computer” to play against as an option). Furthermore, math games support the needs of diverse learners as games can be fun and engaging for students with LD and their typical peers. Math games can be tailored to students’ individual needs and can include scaffolds to support students at their skill level. Online math games are flexible and can incorporate student interest by allowing students to choose games they enjoy playing while still providing practice opportunities on targeted math skills (Buchheister et al., 2017).

Scenario

A fourth-grade student has an LD in mathematics. His multidisciplinary evaluation team noted that he struggles with multiplication, particularly with being fluent (i.e., it took him a significant amount of time to solve the problems compared with his peers). His special education teacher also found that he “shuts down” with worksheets and flashcards but loves to play games. The teacher turned to the NCII website to look into mathematics interventions and found that games are an evidence-based practice to support mathematics. Several games were identified, but he felt the Product Game, a game from the Connected Mathematics Project (CMP) curriculum and available virtually from the NCTM, would provide the best support (Lappan et al., 2014). The Product Game would support the student in multiplication at school as well as at home. The entire class first learns to play the game using explicit instruction. After a period of time, the teacher determines that playing the game has increased multiplication fluency within the class. Likewise, the student exhibits increased engagement and confidence in mathematics. Playing the games with his peers has also helped create stronger interpersonal relationships with his peers, who now ask to be his partner in class for a variety of activities.

Explicit instruction advanced organizer

Today we are going to play the product game. This game focuses on multiplication and allows you to practice your multiplication facts. Multiplication is important because you use it every day when you go shopping, pay for your meal at a restaurant, build something, and even when you’re cooking.

Explicit instruction model

First, I am going to play the game to show you what to do and explain the rules. This is the gameboard; it has numbers from 1 to 81 listed here with each number having its own square. The object of the game, or what you are trying to do, is fill in four boxes in a row. The first person to fill in four boxes in a row, wins. You can fill in four boxes vertically, horizontally, and diagonally. To fill in boxes you will move the sliders at the bottom of the screen to the different factors. It takes two factors to make a product, so if my opponent goes first they do not get to fill in a box as each turn you will only get to move one slider. In my example here, my opponent, the computer, chose to start their slider on the number 4, and now it is my turn. I think I want to fill in the number 12. I know that 4 × 3 = 12 so I am going to move my slider to the number 3. Now, on my next turn I want to try to fill in a number that can help me get 4 in a row or try to block my opponent.

The instructor continues explaining rationale for each move made as the games is played stressing vocabulary and concepts such as factors, multiples, products, and multiplication.

Explicit instruction guided

Now, I want you to play the game against the computer. I will be here to help you but I want you to play on your own. I encourage you to talk about your moves like I did so I can hear what you’re thinking.

If the student makes a mistake, the instructor provides a prompt. For example, if the student attempts to move both of the sliders on their turn instead of just one say “remember you only move one slider per turn.”

Explicit instruction independent

“Now, since you know how to play, I want you to play on your own either with a partner or against the computer.” In the independent portion, students who have been successful in the guided portion (set a mastery criteria such as fewer than two prompts in guided) will play the game independently and the teacher should be nearby to monitor and provide feedback.

Conclusion

With the increasing access to technology in mathematics classrooms, it is important for teachers to be aware of different digital tools available, why these tools are effective practices, and how to implement them in their classrooms to support students with LD. Among the many digital technology options available, digital calculators and online games are versatile and effective tools to support students with LD across a variety of mathematics skills and concepts. For students with LD, the use of technology in mathematics is considered a best practice, but only if the technology selected is intentionally based on what, why, how, and under what conditions the technology can be used to support students’ specific needs. Teachers should consider the digital tools presented in this column as options to incorporate into the classroom to support students with LD in mathematics.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Holly M. Long

Notes

References

Bay-Williams

J. M.

SanGiovanni

J. J.

(2021). Figuring out fluency in mathematics teaching and learning: Moving beyond basic facts and memorization. Grades K-8. Corwin.

Bouck

E. C.

Bouck

M. K.

Hunley

(2015). The calculator effect: Understanding the impact of calculators as accommodations for secondary students with disabilities. Journal of Special Education Technology, 30(2), 77–88. https://doi.org/10.1177/0162643415617371

Boyle

J. R.

Kennedy

M. J.

(2019). Innovations in classroom technology for students with disabilities. Intervention in School and Clinic, 55(2), 67–70. https://doi.org/10.1177/1053451219837716

Buchheister

K. E.

Jackson

Taylor

C. E.

(2017). Math games: A universal design approach to math reasoning. Australian Primary Mathematics Classroom, 22(4), 7–12.

Burrill

Allison

Breaux

Kastberg

Keatham

Sanchez

(2002). Handheld graphing technology at the secondary level: Research findings and implications for classroom practice. Texas Instruments.

CAST. (2018). Universal design for learning guidelines-version 2.2. CAST. http://udlguidelines.cast.org

Chambers

(2020). Assistive technology supporting inclusive education: Existing and emerging trends. In Chambers

(Ed.), Assistive technology to support inclusive education (pp. 1–17). Emerald.

Doabler

C. T.

Fien

(2013). Explicit mathematics instruction: What teachers can do for teaching students with mathematics difficulties. Intervention in School and Clinic, 48(5), 276–285. https://doi.org/10.1177/1053451212473151

Ellington

A. J.

(2003). A meta-analysis of the effects of calculators on students’ achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5), 433–463. https://doi.org/30034795

10.

Kennedy

M. J.

Boyle

J. R.

(2021). That really escalated quickly: Online learning move into the mainstream. Journal of Special Education Technology, 36(2), 63–66. https://doi.org/10.1177/01626434211006052

11.

Lai

S. A.

Berkeley

(2012). High-stakes test accommodations: Research and practice. Learning Disability Quarterly, 35(3), 158–169. https://doi.org/10.1177/0731948711433874

12.

Lappan

Phillips

E. D.

Fey

J. T.

Friel

S. N.

(2014). Connected mathematics project (3rd ed.). Savvas Learning Company.

13.

Marino

M. T.

Tsurusaki

B. K.

Basham

J. D.

(2011). Selecting software for students with learning and other disabilities. Science Teacher, 78(3), 70–72.

14.

McConomy

M. A.

Root

Wade

(2021). Using task analysis to support inclusion and assessment in the classroom. Teaching Exceptional Children. Advance online publication. https://doi.org/10.1177/00400599211025565

15.

McDonald

P. A.

Berg

D. H.

(2018). Identifying the nature of impairments in executive functioning and working memory of children with severe difficulties in arithmetic. Child Neuropsychology, 24(8), 1047–1062. https://doi.org/10.1080/09297049.2017.1377694

16.

McLeskey

Barringer

M.-D.

Billingsley

Brownell

Jackson

Kennedy

Lewis

Maheady

Rodriguez

Scheeler

M. C.

Winn

Ziegler

(2017, January). High-leverage practices in special education. Council for Exceptional Children & CEEDAR Center.

17.

Mellott

J. A.

Adrion

S. P.

(2019). Using brief experimental analysis to identify the right math intervention at the right time. Journal of Behavioral Education, 28(1), 435–455. https://doi.org/10.1007/s10864-019-09324-x

18.

Moyer-Packenham

P. S.

Lommatsch

C. W.

Litster

Ashby

Bullock

E. K.

Roxburgh

A. L.

Shumway

J. F.

Speed

Covington

Hartmann

Clarke-Midura

Skaria

Westenskow

MacDonald

Symanzik

Jordean

(2019). How design features in digital math games support learning and mathematics connections. Computers in Human Behavior, 91(1), 316–332. https://doi.org/10.1016/j.chb.2018.09.036

19.

National Center on Intensive Intervention. (2016). Principles for designing intervention in mathematics. Department of Education. https://intensiveintervention.org/sites/default/files/Princip_Effect_Math_508.pdf

20.

National Council of Teachers of Mathematics. (2000). Principles, standards, and expectations. [Position Statement]. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Principles,-Standards,-and-Expectations/

21.

National Council of Teachers of Mathematics. (2015). Strategic use of technology in teaching and learning mathematics. [Position statement]. https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/Strategic%20Use%20of%20Technology%20July%202015.pdf

22.

Nelson

Powell

S. R.

(2017). A systematic review of longitudinal studies of mathematics difficulty. Journal of Learning Disabilities, 51(6), 523–539. https://doi.org/10.1177/0022219417714773

23.

M. W.

Bryant

D. P.

Bryant

(2019). Effects of computer-assisted instruction on the mathematics performance of students with learning disabilities: A synthesis of the research. Exceptionality, 28(1), 30–44. https://doi.org/10.1080/09362835.2019.1579723

24.

M. W.

Kim

M. K.

Kang

E. Y.

Bryant

B. R.

(2016). How to find good apps: An evaluation rubric for instructional apps for teaching students with learning disabilities. Intervention in School and Clinic, 51(4), 244–252. https://doi.org/10.1177/1053451215589179

25.

Rutherford

(2015). Why play math games?. National Council of Teachers of Mathematics. https://www.nctm.org/Publications/TCM-blog/Blog/Why-Play-Math-Games_/

26.

Technical Education Research Centers. (2016). Investigations in number, data, and space (3rd ed.). Savvas Learning Company.

27.

Thomas

C. N.

Peeples

K. N.

Kennedy

M. J.

Decker

(2019). Riding the special education technology wave: Policy, obstacles, recommendations, actionable ideas, and resources. Intervention in School and Clinic, 54(1), 295–303. https://doi.org/10.1177/10534518819201

28.

Watson

S. M. R.

Gable

R. A.

(2013). Unraveling the complex nature of mathematics learning disability: Implications for research and practice. Learning Disability Quarterly, 36, 156–165. https://doi.org/10.1177/0731948712461489