Does finger sense predict addition performance?

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<ul><li><p>RESEARCH REPORT</p><p>Does finger sense predict addition performance?</p><p>Sharlene D. Newman1</p><p>Received: 25 November 2015 / Accepted: 1 March 2016</p><p> Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2016</p><p>Abstract The impact of fingers on numerical and math-</p><p>ematical cognition has received a great deal of attention</p><p>recently. However, the precise role that fingers play in</p><p>numerical cognition is unknown. The current study</p><p>explores the relationship between finger sense, arithmetic</p><p>and general cognitive ability. Seventy-six children between</p><p>the ages of 5 and 12 participated in the study. The results of</p><p>stepwise multiple regression analyses demonstrated that</p><p>while general cognitive ability including language pro-</p><p>cessing was a predictor of addition performance, finger</p><p>sense was not. The impact of age on the relationship</p><p>between finger sense, and addition was further examined.</p><p>The participants were separated into two groups based on</p><p>age. The results showed that finger gnosia score impacted</p><p>addition performance in the older group but not the</p><p>younger group. These results appear to support the</p><p>hypothesis that fingers provide a scaffold for calculation</p><p>and that if that scaffold is not properly built, it has con-</p><p>tinued differential consequences to mathematical</p><p>cognition.</p><p>Keywords Finger gnosia Cognition Number Arithmetic</p><p>Introduction</p><p>Mathematical competence, like all of cognition, begins</p><p>early and has a neurological basis that is itself linked to the</p><p>active experiences of children. It is a general and well</p><p>accepted fact that the activities that we engage in have a</p><p>direct impact on brain development and future cognitive</p><p>processing (Greenough et al. 1987). This is particularly</p><p>true of children due to the rapid neural development that</p><p>takes place. Here, we focus on finger processing and its</p><p>relationship to mathematical competence. Because finger</p><p>use as well as finger sense has been shown to positively</p><p>predict mathematical achievement in children (Fayol et al.</p><p>1998; Noel 2005; Chinello et al. 2013; Penner-Wilger et al.</p><p>2007, 2008), it is important to understand its precise role in</p><p>mathematical cognition. This is especially important</p><p>because several studies (Penner-Wilger et al. 2007, 2008;</p><p>Fuson et al. 1982; Fuson 1988; Butterworth 1999a, b,</p><p>2005) suggest that finger processing may play a role in</p><p>setting up the neural networks on which more advanced</p><p>mathematical computations are built.</p><p>The relationship between fingers and number has</p><p>received a great deal of attention recently. It has been</p><p>assumed that fingers play a significant role in the devel-</p><p>opment of a mature counting system (Fuson et al. 1982;</p><p>Fuson 1988; Butterworth 1999a, b, 2005). There are a</p><p>number of hypotheses to account for the role of fingers in</p><p>number processing: they are a memory aid during counting</p><p>(Fuson et al. 1982); they aid in understanding cardinality</p><p>(Fayol and Seron 2005); in the development of the one-to-</p><p>one correspondence principle (Alibali and DiRusso 1999),</p><p>among others. Additionally, it has been suggested that</p><p>finger counting habits may influence the way numbers are</p><p>represented and processed (Pesenti et al. 2000; Zago et al.</p><p>2001; Fias and Fischer 2005; Di Luca et al. 2006; Fischer</p><p>Handling editor: Martin H. Fischer, University of Potsdam, Germany.</p><p>Reviewers: Marco Fabbri, Second University of Naples, Italy; Ilaria</p><p>Berteletti, University of Illinois at Urbana-Champaign, USA.</p><p>&amp; Sharlene D.</p><p>1 Department of Psychological and Brain Sciences, Indiana</p><p>University, Bloomington, IN 47405, USA</p><p>123</p><p>Cogn Process</p><p>DOI 10.1007/s10339-016-0756-7</p><p>;domain=pdf;domain=pdf</p></li><li><p>2006; Domahs et al. 2010; Newman and Soylu 2014; Sato</p><p>et al. 2007).</p><p>Furthermore, there has been some suggestion that finger</p><p>sense may play a role in arithmetic as well as number</p><p>processing. A number of studies have confirmed Gerst-</p><p>manns (1940) findings of an association between finger</p><p>agnosia and arithmetic. For example, Reeves and Hum-</p><p>berstone (2011) demonstrated that finger sense changed</p><p>between the ages of 5 and 7 and that those changes were</p><p>related to finger use in arithmetic computation, suggesting</p><p>an important role for finger sense in arithmetic. Addition-</p><p>ally, Fischer and Brugger (2011) hypothesize that fingers</p><p>are important for setting up the space number associations</p><p>which have been shown to be extremely important in</p><p>mathematical cognition from magnitude processing to</p><p>calculation. These studies along with others demonstrate</p><p>the importance of fingers in mathematical cognition.</p><p>However, the underlying mechanism that supports this</p><p>relationship is unclear.</p><p>There is a growing body of research that suggests the use</p><p>of concrete materials aids classroom learning, particularly in</p><p>math (Suh 2007; Thompson 1994; Fuson 1990; Fuson and</p><p>Briars 1990). The use of manipulatives is thought to help</p><p>students think, reason, and solve problems (Burns 1996,</p><p>p. 48). They are an additional resource for helping students</p><p>construct ideas, giving meaning to mathematical concepts</p><p>and subsequently facilitating performance (Sternberg and</p><p>Grigorenko 2004). Fingers are, in essence, a manipulative</p><p>that is always present and that has a well-connected internal</p><p>representation. Fingers are a part of the body, always pre-</p><p>sent; they do the manipulating (with other manipulatives</p><p>such as counting counters or pieces of fraction pies). They</p><p>allow for physical interaction with number (e.g., they can be</p><p>moved) which has been shown to enhance memory and</p><p>understanding (Glenberg et al. 2004) and because of their</p><p>constant availability, experiences with fingers in number</p><p>contexts are likely to far exceed other concrete aids. For</p><p>example, in a recent study using the iCub child-like robot, it</p><p>was found that number knowledge was more efficiently</p><p>learned when number words are learned with finger count-</p><p>ing as opposed to without finger counting (De La Cruz et al.</p><p>2014). If a similar mechanism is at play for children, fingers</p><p>may be a good tool to aid number learning.</p><p>In order to examine the impact of finger processing on</p><p>mathematical competency the current study examined the</p><p>relationship between finger sense, arithmetic performance</p><p>and general cognitive ability in a group of children between</p><p>the ages of five and twelve. The first goal of the current</p><p>study was to assess how cognitive ability interacts with</p><p>addition performance and finger sense. The general cog-</p><p>nitive abilities examined included phonological processing,</p><p>short-term and working memory as well as verbal and non-</p><p>verbal IQ. These measures were chosen because they have</p><p>previously been shown to be correlated with mathematical</p><p>performance (De Smedt et al. 2009; Jordan et al. 2010;</p><p>Passolunghi and Lanfranchi 2012; Passolunghi and Siegel</p><p>2004; Passolunghi et al. 2007; Robinson et al. 2002; Imbo</p><p>and Vandierendonck 2007). However, few studies have</p><p>explored how all of these factorsage, finger sense, gen-</p><p>eral cognitive ability and mathematical abilityinteract.</p><p>Based on previous work, it was expected that age would</p><p>correlate with all factors, but that finger sense and cogni-</p><p>tive ability would have independent relationships with</p><p>arithmetic performance.</p><p>The second aim explored here was to test the hypothesis</p><p>that fingers provide a natural scaffold for calculation</p><p>(Jordan et al. 2008). In other words, fingers may provide the</p><p>support necessary to build calculation skills; it is founda-</p><p>tional to mathematical competency. To explore this</p><p>hypothesis, the relationship between age, finger sense and</p><p>addition performance was further explored. As Reeves and</p><p>Humberstone (2011) reported, finger sense is still develop-</p><p>ing during the early elementary school years; however, it</p><p>may be expected to be somewhat stable at older ages. Along</p><p>with the development of finger sense, addition skill is also</p><p>being developed in younger children. A recent study by</p><p>Berteletti et al. (2015) found a relationship between sub-</p><p>traction performance and finger related activation in</p><p>somatosensory cortex. They argued that children with lower</p><p>performance engaged finger processing areas more than</p><p>children with higher performance. Because age was corre-</p><p>lated with subtraction accuracy, this differential involve-</p><p>ment of finger processingmay be a function of development.</p><p>Therefore, studying both a younger (58 years old) and</p><p>older group (912 years old) will allow for the examination</p><p>of the importance of the finger scaffold in both the early</p><p>learning of addition as well as the later instantiated addition</p><p>skill of older children. Based on previous findings, it was</p><p>expected that younger children would show a stronger</p><p>relationship between finger sense and arithmetic processing</p><p>performance than older children who may be expected to</p><p>have developed more mature retrieval strategies.</p><p>Methods</p><p>Participants</p><p>Seventy-six children (512 years of age, M = 8.67 2,</p><p>36 males) participated in the study for pay. Participants all</p><p>attended local schools and had no history of neurological or</p><p>psychiatric disorders or diagnosed dyslexia or dyscalculia</p><p>as reported by parents. Written informed consent was</p><p>obtained from parents and assent from each participant, as</p><p>approved by the Institutional Review Board of Indiana</p><p>University, Bloomington.</p><p>Cogn Process</p><p>123</p></li><li><p>Measures</p><p>Finger gnosia</p><p>The finger gnosia test is a standard assessment that dates</p><p>back to Benton (1955). During the test, participants sat</p><p>with both hands palm down on the table in front of them.</p><p>They were instructed to close their eyes and to keep them</p><p>closed during the entire procedure (eyes were checked</p><p>regularly). There were two phases of the test. During the</p><p>first phase, the experimenter, with a pointer, touched a</p><p>single finger of the left hand in a pre-determined order,</p><p>touching each finger (5 trials). After each finger touch the</p><p>subject was instructed to indicate by moving the corre-</p><p>sponding finger of the other hand (1 point per trial). During</p><p>the second phase, the experimenter touched a combination</p><p>of two fingers in succession (5 trials) and the participant</p><p>was instructed to indicate which two fingers were touched</p><p>and the order that they were touched by moving the cor-</p><p>responding fingers of the other hand (2 points per trial; 1</p><p>point for the correct fingers and 1 point for the correct</p><p>order). The score was the total number of points earned</p><p>divided by the total possible points. There were 15 possible</p><p>points.</p><p>Handedness</p><p>The Edinburgh Handedness Inventory (Oldfield 1971) was</p><p>administered to each participant. Each question was read to</p><p>the participant, and they demonstrated how they would</p><p>perform the task. For example, for the question which hand</p><p>do you use to throw a ball? The participant would be</p><p>encouraged to simulate throwing. All subjects were right-</p><p>handed.</p><p>Digit span</p><p>The forward (FDS) and backward digit span (BDS) tasks</p><p>were administered to assess short-term and working</p><p>memory, respectively. For both, a series of digits were read</p><p>to the participant at a constant pace starting with two digits</p><p>and increasing by a single digit until failure to recall occurs</p><p>twice. For the FDS, participants were told to repeat the</p><p>digits in the order read. For the BDS, they were told to</p><p>repeat the digits in the reverse order read. The score was</p><p>the percent correct.</p><p>Word attack</p><p>The word attack (Woodcock et al. 2001) task was admin-</p><p>istered to assess phonological skills. The initial items</p><p>require participants to produce the sounds for single letters.</p><p>Afterward, difficulty increases. For the remaining items</p><p>they were required to read aloud letter combinations that</p><p>are phonically consistent patterns in English but are non-</p><p>words or low frequency words. The score was the percent</p><p>correct.</p><p>Vocabulary</p><p>The vocabulary subtest of the Wechsler Intelligence Scale</p><p>for Children was administered as a test of verbal IQ. This</p><p>test measures verbal fluency, concept formation, word</p><p>knowledge and usage. It is an untimed test in which par-</p><p>ticipants are read a word and are asked to define it. The</p><p>score was the percent correct.</p><p>Matrix reasoning</p><p>The matrix reasoning subtest of the Wechsler Intelligence</p><p>Scale for Children was administered as a test of non-verbal</p><p>IQ. This test measures visual processing and abstraction</p><p>and spatial perception. Children are shown colored matri-</p><p>ces or visual patterns with something missing. The child is</p><p>then asked to select the missing piece from a range of</p><p>options. The score was the percent correct.</p><p>Timed addition test</p><p>Participants were presented with 40 single-digit addition</p><p>problems and given 1 min to complete as many as they</p><p>can. The problems were organized with easy problems</p><p>presented first with problems becoming more difficult, with</p><p>difficulty being defined by the size of the operands (all 9 or</p><p>less). Therefore, the largest magnitude of the answers was</p><p>18. No tie problems were presented (e.g., 2 ? 2). The total</p><p>percent correct (out of 40) and the number of problems</p><p>attempted were examined.</p><p>Results</p><p>No significant relationship was found between any of the</p><p>factors and gender or handedness. As a result, neither was</p><p>further considered.</p><p>Multiple regression analysis</p><p>A stepwise multiple regression analysis using the PHREG</p><p>procedure in SAS was performed. The independent vari-</p><p>ables examinedage, word attack, finger gnosia, FDS,</p><p>BDS, vocabulary and matrix reasoningwere entered into</p><p>the analysis to determine which predicted performance on</p><p>the timed addition task. The stepwise selection process</p><p>resulted in a model with four explanatory variablesage,</p><p>word attack, FDS and BDS. The model with these four</p><p>Cogn Process</p><p>123</p></li><li><p>variables explained 61 % of the variance [F(4,71) =</p><p>28.31, p\ 0.0001, MSE = 0.561, R2 = 0.6147].</p><p>Effect of age</p><p>Because age is expected to be responsible for a large</p><p>portion of the variance in addition performance, a second</p><p>analysis designed to explore the impact of age on the</p><p>relationship between finger gnosia and addition perfor-</p><p>mance examined older and younger children separately.</p><p>The subjects were divided into two groups based on age:</p><p>older group (N = 42; M = 10.2 1.01), younger group</p><p>(N = 34; M = 6.7 1.1). A stepwise multiple regression</p><p>analysis was performed on each group separately. For the</p><p>older group vocabulary, matrix reasoning and forward digit</p><p>span significantly predicted addition performance</p><p>[F(1,40) = 5.09, p\ 0.005; accounted for 29 % of thevariance]. For the younger group, age and word attack</p><p>predicted addition performance [F(1,32) = 17.29,</p><p>p\ 0.001; accounted for 54 % of the variance].Finally, because one of the primary aims of the study</p><p>was to explore the relationship between finger sense and</p><p>arithmetic, this relationship was further explored. First, a</p><p>correlation analysis was performed with age partialled out</p><p>(see Fig. 1). In the full dataset the correlation between</p><p>finger gnosia and addition performance was significant</p><p>before controlling for age (r = 0.36), after controlling for</p><p>age the correlation was only trending (r...</p></li></ul>


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