# Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

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## Abstract

**:**

## 1. Introduction

#### 1.1. Neural Networks for Arithmetic

**Subtraction versus multiplication.**So far, we have discussed brain activations related to procedure-based calculation on the one hand and verbal memory-based arithmetic fact retrieval on the other hand, but we have not yet associated these two processing types with specific arithmetic operations (addition, subtraction, multiplication and division). A wealth of behavioral research shows that the processing type used by proficient adults to solve arithmetic tasks is strongly affected by the type of operation [50,51]. For example, typical adults are more likely to solve subtraction than multiplication problems using procedure-based calculation processes, i.e., manipulating the relations between numbers [52], requiring access to the semantic meaning of quantities behind the numbers. In contrast, for multiplication they are more likely to use verbal memory-based arithmetic fact retrieval [53,54].

#### 1.2. Developmental Dyscalculia

**Neural networks activated during arithmetic in DD.**Impaired arithmetic performance in developmental dyscalculia has often been linked to abnormal brain activations in the parietal lobe. However, as far as we are aware, the existing literature on abnormal brain activation during arithmetic in DD is based entirely on studies with children whose arithmetic skills might still be developing. Compared to typically developing children, children with DD [100] showed reduced activation in parietal, visual and prefrontal regions during addition. Parietal under-activation was reported in the right IPS, the right PSPL and the right angular gyrus. Reduced brain activation in children with DD has also been reported during subtraction in the left posterior and inferior parietal lobe [101]. In the same study a classifier was able to distinguish between children with DD and controls based on their activation pattern during subtraction in the angular and inferior frontal gyrus. Finally, reduced activation in children with DD has also been reported for multiplication [102] in the right IPS, SPL and inferior parietal lobe as well as in the left inferior frontal gyrus, and the left middle and superior temporal gyri.

#### 1.3. The Current Study

**Hypotheses.**First, for the control group we expected stronger activation in the typical bilateral fronto-parietal math-responsive network of procedure-based calculation during subtraction and in the left lateralized arithmetic fact retrieval network of perisylvian language areas centered around the left AG during multiplication. Furthermore, we predicted stronger activations in bilateral IPS and PSPL for subtraction than multiplication and stronger activation in the left AG during multiplication than subtraction.

## 2. Materials and Methods

#### 2.1. Participants

#### 2.1.1. Single Case

#### 2.1.2. Control Group

#### 2.2. Stimuli

#### 2.2.1. Background Measures

**General cognitive ability.**The cognitive abilities of the participants were estimated using the Wechsler Abbreviated Scale of Intelligence (WASI; [109]). A total of 16 participants (including RM) were tested on all four subtests (Vocabulary, Block Design, Similarities, Matrix Reasoning); for 3 control participants, we estimated their cognitive ability based on their performance on two subtests (Vocabulary, Matrix Reasoning).

**Arithmetic.**Arithmetic ability was assessed using the Wide Range Achievement Test (WRAT-3 Arithmetic [104]) arithmetic subtest. Participants were given 15 min to work through the 40 mathematical problems of increasing difficulty (from additions, subtractions, multiplications, divisions, fractions, to the use of decimal numbers, and algebra).

**Reading skills.**The participants’ ability to pronounce printed words accurately and fluently was assessed with the word (Sight Word Efficiency) and nonword (Phonemic Decoding) subtests of the Test of Word Reading Efficiency (TOWRE; [110]). Reading and spelling accuracy were established by administering the Reading and Spelling Subtests of the Wide Range Achievement Test (WRAT–3 Reading, WRAT–3 Spelling; [104]).

**Working memory.**We tested RM and 10 control participants on two tests from the Wechsler Memory Scale (WMS–III; [111]): Digit Span Forward and Digit Span Backward. In Digit Span Forward, participants heard sequences of numbers increasing in length and had to repeat them verbatim. During Digit Span Backward they also heard sequences of digits but had to repeat them in reverse order. In both tests, sequences increased in length until the participant recited two sequences of the same length incorrectly, at which point the testing finished. To assess nonverbal memory skills, participants were tested on the Spatial Span Forward and Spatial Span Backward subtests of the Wechsler Memory Scale (WMS–III), which are spatial analogues of the Digit Span tests. A board that had nine 3-dimensional cubes placed on it was shown to the participants. The experimenter pointed to a sequence of cubes one after the other. The participant had to remember the sequence and repeat it either in the order presented (Spatial Span Forward) or in reverse order (Spatial Span Backward). Sequences increased in length until participants produced two sequences of the same length incorrectly.

**Handedness.**Participants’ handedness was assessed with the Edinburgh Handedness Inventory [112].

#### 2.2.2. fMRI Tasks

**Subtraction:**Half of the subtraction trials were problems with a small problem size, i.e., the first operand was a double digit ranging from 11 to 19, and the second operand was a single digit ranging from 3 to 9. The other half had a large problem size, i.e., the first operand ranged from 52 to 91 and the second from 23 to 76. Overall, 80 subtraction trials were presented.

**Multiplication:**All multiplication items (n = 80) used only single-digit operands from 2 to 9. Half of the incorrect solutions were table-related (e.g., the incorrect answer is from the same times table, e.g., 2 × 8 = 14) and half were table-unrelated (e.g., 2 × 8 = 17).

**Control:**For both the subtraction and multiplication task, each problem had a corresponding control item (see Figure 1, panels c and d) which showed the same operands with the arithmetic operational signs replaced by a non-numerical symbol (@). The participants had to judge whether the digits after the second @ were in the same order as the digits presented before. Correct control items (50%) showed the operands after the second @ in the same correct order (e.g., 15 @ 8 @ 158), incorrect control items (50%) in the reversed order (e.g., 15 @ 8 @ 815). These control items were chosen to control for supporting task components (e.g., reading, number processing, decision making and manual responses) without performing an arithmetic operation.

#### 2.2.3. MRI/fMRI Acquisition

^{3}, slice thickness = 3.5 mm, flip angle = 90°).

^{3}, slice thickness = 1 mm, flip angle = 8°). For two control participants, the voxel size was 1 × 1.13 × 1.13 mm

^{3}.

#### 2.3. Procedure

#### 2.4. Data Analyses

#### 2.4.1. Behavioral Analyses

#### 2.4.2. fMRI Analysis

**Data pre-processing.**All fMRI data were analyzed using FEAT (FMRI Expert Analysis Tool, Version 6.00) part of FSL (FMRIB’s Software Library [115]). The Brain Extraction Tool (BET [116]) was used to extract the brain from EPI data, and a temporal high pass filter of 0.02 Hz was applied. The images were motion-corrected using MCFLIRT [117], slice timing corrected, and a Gaussian smoothing kernel of FWHM 5 mm was applied. The functional images were registered to the individual’s structural T1 scans using FLIRT [117,118] and were co-registered to a standard 2 mm MNI152 brain using FNIRT nonlinear registration [119].

**Single-subject analysis.**Individual participants’ whole-brain responses were modeled using a general linear model with each experimental condition (e.g., multiplication trials, multiplication controls trials) used as a regressor. The regressors were defined as the trial duration (3000 ms) convolved with FSL’s canonical gamma hemodynamic response function. Only trials on which participants responded correctly were included in the analysis. Our data analyses focused only on items which presented correct solutions and on the following contrasts of parameter estimates (COPEs): multiplication > multiplication control, subtraction > subtraction control, multiplication minus multiplication control > subtraction minus subtraction control (for simplicity called multiplication > subtraction) and vice versa (for simplicity called subtraction > multiplication). The two scanning sessions were first analyzed separately for each participant and then combined separately for each participant by using a fixed-effect analysis, thresholded at p < 0.05.

**High-level whole-brain analysis.**For each of the contrasts, the COPE files created from the combined subtraction/multiplication analyses for all control group participants were combined to calculate a group mean activation using a mixed effect analysis with FLAME [120]. The statistical maps were corrected for multiple comparisons using a cluster threshold method with a Z threshold of 2.3 and a cluster p threshold of p < 0.05. Due to large clusters being identified, the analyses of subtraction > control and subtraction > multiplication were re-run with a Z threshold of 3.1. To investigate differences between the single case RM and the control group, a second FLAME analysis [120] was run, including RM as a separate group for each contrast of the original analysis. This identified areas of higher activation for the control group than RM and areas of higher activation for RM compared to the control group in the multiplication and subtraction tasks. These statistical maps were also corrected for multiple comparisons and used the same threshold as the control group mean analysis (Z = 2.3 and cluster p < 0.05).

**Regions of interest (ROI) analysis.**In the Regions of Interest (ROI) analysis we focused on brain regions for which we had clear predictions of significant differences in brain activation between RM and the control group. These areas were four areas in each hemisphere: the intraparietal sulcus (IPS), the angular gyrus (AG), the posterior superior parietal lobule (PSPL) and the primary motor cortex. These areas were defined using the Jülich Histological Atlas [121,122,123]. The Jülich Atlas splits these regions into further anatomical subregions based on probabilistic cytoarchtectonic maps: the IPS into hIP1, hIP2 and hIP3 [124,125], the PSPL into 7A, 7M, 7PC and 7P [125], the angular gyrus into PGa and PGp [126] and the motor cortex into 4a and 4p [127]. For our ROI analyses we calculated the mean percentage BOLD signal change for each subregion and then averaged across the subregions.

## 3. Results

#### 3.1. Behavioral Results

#### 3.1.1. Background Measures

#### 3.1.2. Behavioral Results of the Calculation Tasks Performed in the fMRI Scanner

**Control group only.**Two repeated-measures analyses of variance (ANOVAs) with item type (multiplication, subtraction) and task (calculation, control) as within-subject factors were conducted on mean accuracy and mean RTs of correct responses. Overall, control participants were significantly more accurate on control than calculation items (F (1.17) = 41.758, p < 0.001, η

_{p}

^{2}= 0.711) and more accurate on multiplication than subtraction items (F (1.17) = 34.571, p < 0.001, η

_{p}

^{2}= 0.670). The interaction was also significant (F (1.17) = 36.150, p < 0.001, η

_{p}

^{2}= 0.680), indicating that accuracy on the subtraction calculation items was particularly low. As expected, response times were significantly faster on control than calculation items (F (1.17) = 113.301, p < 0.001, η

_{p}

^{2}= 0.870). Control participants took significantly longer to respond to subtraction than to multiplication items (F (1.17) = 147.480, p < 0.001, η

_{p}

^{2}= 0.897). The interaction was also significant (F (1.17) = 66.112, p < 0.001, η

_{p}

^{2}= 0.795), indicating that response times on the subtraction calculation items were particularly slow.

**Comparison between RM and control group.**RM’s accuracy was significantly lower than the average accuracy of the control group for both types of calculation trials (multiplication and subtraction). However, after correcting for multiple comparisons, this difference remained significant only for multiplication calculation trials. RM’s accuracy on both types of control trials (multiplication control, subtraction control) was not significantly different from the control group. While RM’s response times were longer on all trial types, only RM’s response times on the multiplication calculation trials were significantly lower than those of the control group. This difference remained significant after correcting for multiple comparisons.

#### 3.2. fMRI Results

#### 3.2.1. Whole-Brain Analysis

#### Control Group Only

#### Comparison between RM and the Control Group

#### 3.2.2. Regions-of-Interest Analysis (ROI)

#### Control Group Only

_{p}

^{2}= 0.613) and of hemisphere (F (1.17) = 34.25, p < 0.001, η

_{p}

^{2}= 0.668) emerged. There was no significant interaction between task and hemisphere (F (1.17) = 1.297, p = 0.271, η

_{p}

^{2}= 0.071). As can be seen in Table 5, mean percentage signal change was significantly higher for subtraction (left IPS: 0.48% and right IPS: 0.34%) than multiplication (left IPS: 0.27%, right IPS: 0.09%) and mean percentage signal change was higher in the left than in the right IPS for both tasks.

_{p}

^{2}= 0.293). The percentage signal change in the left AG was significantly higher for subtraction (0.12%) than for multiplication (−0.02%).

_{p}

^{2}= 0.312) but no significant effect of hemisphere (F (1.17) = 2.865, p = 0.109, η

_{p}

^{2}= 0.144). Mean percentage signal change in PSPL was higher during subtraction than multiplication. The interaction between task and hemisphere was also significant (F (1.17) = 5.674, p = 0.029, η

_{p}

^{2}= 0.250). The mean percentage signal change during multiplication was smaller in the right PSPL (0.05%) than in the left PSPL in multiplication (0.15%).

#### Comparison between RM and the Control Group

## 4. Discussion

#### 4.1. Arithmetic Networks in Typical Adults during Subtraction and Multiplication

#### 4.2. Arithmetic Networks in an Adults with Developmental Dyscalculia

#### 4.3. Limitations and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Multiplication | Subtraction | ||||||
---|---|---|---|---|---|---|---|

1st Operant | 2nd Operant | Response | Item Type | 1st Operant | 2nd Operant | Response | Item Type |

2 | 7 | 14 | correct | 11 | 4 | 7 | correct |

2 | 7 | 16 | related | 11 | 4 | 5 | incorrect |

7 | 2 | 14 | correct | 11 | 8 | 5 | incorrect |

7 | 2 | 15 | unrelated | 11 | 8 | 3 | correct |

2 | 8 | 16 | correct | 11 | 6 | 3 | incorrect |

2 | 8 | 15 | unrelated | 11 | 6 | 5 | correct |

8 | 2 | 16 | correct | 12 | 9 | 3 | correct |

8 | 2 | 24 | related | 12 | 9 | 1 | incorrect |

3 | 4 | 12 | correct | 12 | 5 | 9 | incorrect |

3 | 4 | 15 | related | 12 | 5 | 7 | correct |

4 | 3 | 12 | correct | 13 | 7 | 6 | correct |

4 | 3 | 10 | unrelated | 13 | 7 | 4 | incorrect |

3 | 6 | 18 | correct | 13 | 6 | 9 | incorrect |

3 | 6 | 17 | unrelated | 13 | 6 | 7 | correct |

6 | 3 | 18 | correct | 14 | 6 | 10 | incorrect |

6 | 3 | 12 | related | 14 | 6 | 8 | correct |

3 | 8 | 24 | correct | 14 | 3 | 9 | incorrect |

3 | 8 | 21 | related | 14 | 3 | 11 | correct |

8 | 3 | 24 | correct | 15 | 8 | 9 | incorrect |

8 | 3 | 22 | unrelated | 15 | 8 | 7 | correct |

3 | 9 | 27 | correct | 15 | 4 | 11 | correct |

3 | 9 | 23 | unrelated | 15 | 4 | 9 | incorrect |

9 | 3 | 27 | correct | 16 | 9 | 7 | correct |

9 | 3 | 36 | related | 16 | 9 | 5 | incorrect |

4 | 6 | 24 | correct | 16 | 3 | 15 | incorrect |

4 | 6 | 20 | related | 16 | 3 | 13 | correct |

6 | 4 | 24 | correct | 17 | 9 | 8 | correct |

6 | 4 | 22 | unrelated | 17 | 9 | 6 | incorrect |

4 | 7 | 28 | correct | 17 | 8 | 11 | incorrect |

4 | 7 | 34 | unrelated | 17 | 8 | 9 | correct |

7 | 4 | 28 | correct | 18 | 5 | 15 | incorrect |

7 | 4 | 21 | related | 18 | 5 | 13 | correct |

4 | 8 | 32 | correct | 18 | 3 | 17 | incorrect |

4 | 8 | 36 | related | 18 | 3 | 15 | correct |

8 | 4 | 32 | correct | 19 | 7 | 12 | correct |

8 | 4 | 26 | unrelated | 19 | 7 | 14 | incorrect |

4 | 9 | 36 | correct | 19 | 7 | 12 | correct |

4 | 9 | 34 | unrelated | 19 | 7 | 10 | incorrect |

9 | 4 | 36 | correct | 19 | 6 | 13 | correct |

9 | 4 | 27 | related | 19 | 6 | 11 | incorrect |

5 | 7 | 35 | correct | 52 | 39 | 13 | correct |

5 | 7 | 30 | related | 52 | 39 | 11 | incorrect |

7 | 5 | 35 | correct | 52 | 35 | 17 | correct |

7 | 5 | 31 | unrelated | 52 | 35 | 15 | incorrect |

5 | 8 | 40 | correct | 58 | 35 | 25 | incorrect |

5 | 8 | 44 | unrelated | 58 | 35 | 23 | correct |

8 | 5 | 40 | correct | 58 | 24 | 36 | incorrect |

8 | 5 | 48 | related | 58 | 24 | 34 | correct |

5 | 9 | 45 | correct | 64 | 46 | 18 | correct |

5 | 9 | 40 | related | 64 | 46 | 16 | incorrect |

9 | 5 | 45 | correct | 64 | 33 | 31 | correct |

9 | 5 | 47 | unrelated | 64 | 33 | 29 | incorrect |

6 | 7 | 42 | correct | 69 | 47 | 24 | incorrect |

6 | 7 | 44 | unrelated | 69 | 47 | 22 | correct |

7 | 6 | 42 | correct | 69 | 36 | 33 | correct |

7 | 6 | 35 | related | 69 | 36 | 35 | incorrect |

6 | 8 | 48 | correct | 73 | 57 | 18 | incorrect |

6 | 8 | 42 | related | 73 | 57 | 16 | correct |

8 | 6 | 48 | correct | 73 | 46 | 27 | correct |

8 | 6 | 52 | unrelated | 73 | 46 | 25 | incorrect |

7 | 8 | 56 | correct | 75 | 48 | 29 | incorrect |

7 | 8 | 58 | unrelated | 75 | 48 | 27 | correct |

8 | 7 | 56 | correct | 75 | 34 | 39 | incorrect |

8 | 7 | 48 | related | 75 | 34 | 41 | correct |

7 | 9 | 63 | correct | 86 | 59 | 27 | correct |

7 | 9 | 56 | related | 86 | 59 | 25 | incorrect |

9 | 7 | 63 | correct | 86 | 43 | 45 | incorrect |

9 | 7 | 61 | unrelated | 86 | 43 | 43 | correct |

8 | 9 | 72 | correct | 87 | 69 | 18 | correct |

8 | 9 | 76 | unrelated | 87 | 69 | 16 | incorrect |

9 | 8 | 72 | correct | 87 | 58 | 31 | incorrect |

9 | 8 | 81 | related | 87 | 58 | 29 | correct |

3 | 7 | 21 | correct | 91 | 38 | 53 | correct |

3 | 7 | 24 | related | 91 | 38 | 51 | incorrect |

7 | 3 | 21 | correct | 91 | 76 | 17 | incorrect |

7 | 3 | 19 | unrelated | 91 | 76 | 15 | correct |

2 | 9 | 18 | correct | 95 | 21 | 76 | incorrect |

2 | 9 | 21 | unrelated | 95 | 21 | 74 | correct |

9 | 2 | 18 | correct | 95 | 28 | 67 | correct |

9 | 2 | 16 | related | 95 | 28 | 65 | incorrect |

## Appendix B

**Figure A1.**Regions of significant BOLD signal change for the control group (sagittal, coronal and axial view from left to right). (

**a**) multiplication > subtraction (cluster threshold Z = 2.3), (

**b**) subtraction > multiplication (cluster threshold Z = 3.1).

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**Figure 1.**Examples of (

**a**) a subtraction trial, (

**b**) a multiplication trial, with the corresponding control trials (panels (

**c**,

**d**)).

**Figure 2.**Overlay of regions of significant BOLD signal change for the control group in dark color and for RM in light color (sagittal, coronal and axial view from left to right). (

**a**) Multiplication versus control (cluster threshold Z = 2.3) (RM in light red, control group in dark red), (

**b**) subtraction versus control (cluster threshold Z = 2.3) (RM in light blue, control group in dark blue).

**Figure 3.**(

**A**) Mean percentage signal change in six ROIs (left and right IPS, left and right AG, and left and right posterior superior parietal lobule) by task (multiplication in red, subtraction in blue) for the control group, (

**B**) Mean percentage signal change during multiplication in the left IPS and the left AG for RM (in green) and the control group (in gray).

**Figure 4.**Regions of significant differences in BOLD signal change between RM and the control group (sagittal, coronal and axial view from left to right). (

**a**) Higher activation for RM than the control group in multiplication versus control (cluster threshold Z = 2.3), (

**b**) Lower activation for RM than the control group in subtraction versus control (cluster threshold Z = 3.1).

**Figure 5.**(

**A**) Cortical networks and processing pathways for magnitude processing (left panel, red) and arithmetic fact retrieval (right panel, dark blue) in adults with and without DD (developed based on [6,49]). The color-changing arrow between the two panels reflects that these two anatomically separate networks operate together as functionally integrated circuits in numerical cognition. (

**B**) Interplay between magnitude processing and arithmetic fact retrieval. A certain amount of fact retrieval is assumed to be involved in arithmetic independent of the difficulty of the task, depicted as the blue rectangle at the bottom. However, the harder a task becomes, the less fact retrieval (blue triangle, variable fact retrieval component) and the more magnitude processing has been assumed (red triangle, variable magnitude processing component). On the other side, an invariant component of mandatorily involved magnitude processing is assumed as well, depicted as the red rectangle at the top of the figure. Abbreviations: AG—angular gyrus; BG—basal ganglia; EC—entorhinal cortex; EC/EmC—external/extreme capsule system; HC—hippocampus; IFG—inferior frontal gyrus; IPS—intraparietal sulcus; LH—left hemisphere; Medial FG—medial frontal gyrus; MTG—middle temporal gyrus; PSPL—posterior superior parietal lobule; SLF—superior longitudinal fascicle; SMA—supplementary motor area; RC—retrospenial cortex; RH—right hemisphere; TH—thalamus; V1—primary visual cortex; VNF—visual number form.

Test | RM | Controls | Significance Test ^{a} | Estimated Effect Size (z cc) ^{b} | B-H Adjusted p’^{c} | |||
---|---|---|---|---|---|---|---|---|

Mean | SD | N | t | p | ||||

Cognitive ability (IQ) ^{d} | 108 | 121.78 | 10.17 | 18 | −1.319 | 0.102 | −1.355 | 0.255 |

Arithmetic (WRAT) ^{d} | 80 | 100.33 | 11.96 | 18 | −1.654 | 0.058 | −1.699 | 0.193 |

Spelling (WRAT) ^{d} | 101 | 111.94 | 4.43 | 18 | −2.405 | 0.014 | −2.471 | 0.140 |

Reading (WRAT) ^{d} | 119 | 113.44 | 6.47 | 18 | 0.836 | 0.207 | 0.859 | 0.259 |

Sight Word Reading (TOWRE) ^{d} | 104 | 103.17 | 9.61 | 18 | 0.084 | 0.467 | 0.086 | 0.467 |

Phonemic Decoding (TOWRE) ^{d} | 103 | 112.67 | 8.70 | 18 | −1.081 | 0.147 | −1.111 | 0.210 |

Digit Span Forward ^{e} | 10 | 12.30 | 1.85 | 10 | −1.188 | 0.133 | −1.246 | 0.266 |

Digit Span Backward ^{e} | 10 | 8.90 | 2.62 | 10 | 0.400 | 0.349 | 0.419 | 0.388 |

Spatial Scan Forward ^{e} | 7 | 10.90 | 1.92 | 10 | −1.936 | 0.042 | −2.030 | 0.210 |

Spatial Scan Backward ^{e} | 8 | 10.90 | 2.43 | 10 | −1.139 | 0.142 | −1.195 | 0.237 |

^{a}Modified t-test from Crawford and Howell [105], one-tailed.

^{b}Crawford et al. [106].

^{c}Benjamini and Hochberg correction [107] for multiple comparisons; adjusted p-values calculated using the method from Jafari and Ansari-Pour [108].

^{d}Standard score.

^{e}Scaled score.

RM | Controls | Significance Test ^{a} | Estimated Effect Size (z cc) ^{b} | B-H Adjusted p’^{c} | |||
---|---|---|---|---|---|---|---|

Mean | SD | t | p | ||||

Percentage Correct (%) | |||||||

Multiplication | 68.75 | 91.25 | 5.86 | −3.737 | 0.0008 | −3.840 | 0.003 |

Multiplication Control | 93.75 | 97.57 | 2.37 | −1.569 | 0.068 | −1.612 | 0.090 |

Subtraction | 57.50 | 78.40 | 10.80 | −1.873 | 0.039 | −1.924 | 0.078 |

Subtraction Control | 96.25 | 97.01 | 2.92 | −0.253 | 0.402 | −0.260 | 0.402 |

Mean Reaction Time (s) | |||||||

Multiplication | 2.815 | 1.63 | 0.30 | 3.867 | 0.0006 | 3.973 | 0.002 |

Multiplication Control | 1.611 | 1.30 | 0.18 | 1.652 | 0.058 | 1.697 | 0.117 |

Subtraction | 2.810 | 2.26 | 0.36 | 1.494 | 0.077 | 1.535 | 0.102 |

Subtraction Control | 1.712 | 1.47 | 0.23 | 1.029 | 0.159 | 1.057 | 0.159 |

Region ^{a} | Number of voxels | Z-max | MNI Coordinates ^{b} | Juelich Histological Atlas ^{c} | ||
---|---|---|---|---|---|---|

x | y | z | ||||

Multiplication > Control * | ||||||

L Inferior Frontal Gyrus | 3906 | 4.75 | −46 | 22 | 20 | Left Broca’s Area (45) |

L Supramarginal Gyrus | 1994 | 4.15 | −44 | −50 | 36 | Left Anterior IPS (hIP1) |

R Frontal Orbital cortex | 1968 | 4.17 | 36 | 28 | −6 | - |

L Paracingulate Gyrus | 1168 | 3.95 | −8 | 10 | 44 | Left Premotor Cortex (Area 6) |

R Cerebellum | 487 | 4.17 | 36 | −68 | −46 | - |

L Thalamus | 434 | 3.36 | −10 | −2 | 8 | - |

Subtraction > Control ** | ||||||

L Inferior Frontal Gyrus | 31222 | 6.28 | −44 | 24 | 22 | Left Broca’s Area (45) |

L Angular Gyrus | 5.95 | −45 | −52 | 54 | Inferior Parietal Lobule (PFm) | |

R Frontal Pole | 5.61 | 35 | 42 | 20 | - | |

R Superior Parietal Lobule | 2736 | 5.16 | 32 | −64 | 38 | Right Superior Parietal (7A) |

R Occipital Pole | 246 | 4.13 | 30 | −90 | −12 | Right Visual Cortex (V3V) |

Multiplication > Subtraction * | ||||||

R Precuneous Cortex | 1247 | 4.02 | 10 | −52 | 22 | Right WM Cingulum |

L Frontal Pole | 452 | 4.24 | −6 | 60 | −12 | - |

Subtraction > Multiplication ** | ||||||

L Supramarginal Gyrus | 7314 | 5.13 | −52 | −42 | 44 | Left Inferior Parietal (PF) |

L Middle Frontal Gyrus | 2309 | 4.89 | −48 | 32 | 26 | Left Broca’s Area (45) |

R Paracingulate Gyrus | 1780 | 5.17 | 6 | 26 | 36 | - |

R Frontal Orbital Cortex | 1445 | 5.07 | 34 | 24 | −8 | - |

L Insular Cortex | 1201 | 4.65 | −30 | 22 | −6 | - |

R Precentral Gyrus | 646 | 4.99 | 32 | −4 | 60 | Right Premotor Cortex (Area 6) |

R Inferior Temporal Gyrus | 375 | 4.18 | 52 | −60 | −14 | Right Visual Cortex (V5) |

R Precentral Gyrus | 262 | 4.22 | 52 | 6 | 24 | Right Broca’s Area (44) |

R Frontal Pole | 197 | 4.04 | 38 | 54 | 18 | - |

Brain Stem | 160 | 3.99 | 0 | −22 | −24 | - |

R Middle Frontal Gyrus | 145 | 3.98 | 48 | 30 | 30 | Right Broca’s Area (45) |

Region ^{a} | Number of Voxels | Z-max | MNI Coordinates ^{b} | Juelich Histological Atlas ^{c} | ||
---|---|---|---|---|---|---|

x | y | z | ||||

Multiplication: RM > Control Group * | ||||||

L Precentral Gyrus | 10053 | 4.67 | −56 | 8 | 12 | Left Broca’s Area (44) |

L Inferior Frontal Gyrus | 4.48 | −52 | 8 | 16 | Left Broca’s Area (44) | |

L Supramarginal Gyrus | 3.01 | −34 | −38 | 38 | Left Anterior IPS (hIP1) | |

L Angular Gyrus | 3219 | 4.34 | −48 | −56 | 40 | Left Inferior Parietal (PGa) |

R Frontal Pole | 633 | 4.36 | 24 | 48 | 24 | - |

R Supramarginal Gyrus | 490 | 3.66 | 64 | −38 | 40 | Right Inferior Parietal (PF) |

Subtraction: Control Group > RM ** | ||||||

R Occipital Fusiform Gyrus | 31742 | 5.10 | 16 | −84 | −18 | - |

R Thalamus | 4.07 | 11 | 1 | 8 | - | |

L Thalamus | 4.05 | −5 | −10 | 8 | - | |

R Middle Frontal Gyrus | 1962 | 4.20 | 44 | 26 | 24 | Right Broca’s Area (45) |

R Frontal Pole | 999 | 3.47 | 28 | 64 | 8 | - |

L Cerebral White Matter | 776 | 3.74 | −28 | 12 | 22 | - |

R Temporal Pole | 590 | 3.44 | 42 | 22 | −22 | - |

R Middle Frontal Gyrus | 456 | 3.89 | 28 | 22 | 38 | - |

R Superior Frontal Gyrus | 421 | 3.44 | 20 | −4 | 66 | Right Premotor Cortex (Area 6) |

**Table 5.**Mean percentage signal change for RM and the control group during multiplication and subtraction by ROI.

Region of Interest | RM | Controls ^{a} | Significance Test ^{b} | Estimated Effect Size (z cc) ^{c} | B-H Adjusted p’ ^{d} | ||
---|---|---|---|---|---|---|---|

Mean | SD | t | p | ||||

Multiplication | |||||||

Left IPS | 0.5535 | 0.2659 | 0.1488 | 1.881 | 0.0386 | 1.933 | 0.3087 |

Right IPS | 0.1944 | 0.0921 | 0.1823 | 0.546 | 0.2960 | 0.561 | 0.3643 |

Left AG | 0.4109 | −0.0201 | 0.1540 | 2.723 | 0.0072 | 2.798 | 0.1157 |

Right AG | −0.0443 | −0.1137 | 0.1783 | 0.382 | 0.3536 | 0.393 | 0.3771 |

Left PSPL | 0.2913 | 0.1482 | 0.1933 | 0.721 | 0.2405 | 0.740 | 0.3498 |

Right PSPL | 0.0965 | 0.0472 | 0.2183 | 0.22 | 0.4143 | 0.226 | 0.4143 |

Left Motor | 0.3111 | 0.0920 | 0.1421 | 1.501 | 0.0759 | 1.542 | 0.2428 |

Right Motor | 0.0598 | −0.1134 | 0.1117 | 1.506 | 0.0752 | 1.547 | 0.3010 |

Subtraction | |||||||

Left IPS | 0.2349 | 0.4835 | 0.1807 | −1.339 | 0.0991 | −1.376 | 0.1982 |

Right IPS | −0.0219 | 0.3397 | 0.2455 | −1.434 | 0.0849 | −1.473 | 0.2263 |

Left AG | −0.0374 | 0.1154 | 0.2336 | −0.663 | 0.2580 | −0.682 | 0.3434 |

Right AG | −0.2273 | −0.0977 | 0.2418 | −0.519 | 0.3051 | −0.533 | 0.3487 |

Left PSPL | −0.1004 | 0.2951 | 0.2335 | −1.647 | 0.0590 | −1.692 | 0.3145 |

Right PSPL | −0.1602 | 0.2759 | 0.3265 | −1.299 | 0.1056 | −1.335 | 0.1877 |

Left Motor | −0.0006 | 0.1451 | 0.1584 | −0.898 | 0.1909 | −0.922 | 0.3055 |

Right Motor | −0.2928 | −0.0623 | 0.1596 | −1.409 | 0.0885 | −1.447 | 0.2022 |

^{a}N = 18.

^{b}Modified t-test from Crawford and Howell [105], one-tailed.

^{c}Crawford et al. [106].

^{d}Benjamini and Hochberg correction [107] for multiple comparisons; adjusted p values calculated using the method from Jafari and Ansari-Pour [108].

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**MDPI and ACS Style**

Göbel, S.M.; Terry, R.; Klein, E.; Hymers, M.; Kaufmann, L.
Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data. *Brain Sci.* **2022**, *12*, 735.
https://doi.org/10.3390/brainsci12060735

**AMA Style**

Göbel SM, Terry R, Klein E, Hymers M, Kaufmann L.
Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data. *Brain Sciences*. 2022; 12(6):735.
https://doi.org/10.3390/brainsci12060735

**Chicago/Turabian Style**

Göbel, Silke M., Rebecca Terry, Elise Klein, Mark Hymers, and Liane Kaufmann.
2022. "Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data" *Brain Sciences* 12, no. 6: 735.
https://doi.org/10.3390/brainsci12060735