Fact Retrieval Research Articles

Frontal and Parietal Cortices Show Different Spatiotemporal Dynamics across Problem-solving Stages.

Arithmetic problem-solving can be conceptualized as a multistage process ranging from task encoding over rule and strategy selection to step-wise task execution. Previous fMRI research suggested a frontal-parietal network involved in the execution of complex numerical and nonnumerical tasks, but evidence is lacking on the particular contributions of frontal and parietal cortices across time. In an arithmetic task paradigm, we evaluated individual participants' "retrieval" and "multistep procedural" strategies on a trial-by-trial basis and contrasted those in time-resolved analyses using combined EEG and MEG. Retrieval strategies relied on direct retrieval of arithmetic facts (e.g., 2 + 3 = 5). Procedural strategies required multiple solution steps (e.g., 12 + 23 = 12 + 20 + 3 or 23 + 10 + 2). Evoked source analyses revealed independent activation dynamics within the first second of problem-solving in brain areas previously described as one network, such as the frontal-parietal cognitive control network: The right frontal cortex showed earliest effects of strategy selection for multistep procedural strategies around 300 msec, before parietal cortex activated around 700 msec. In time-frequency source power analyses, memory retrieval and multistep procedural strategies were differentially reflected in theta, alpha, and beta frequencies: Stronger beta and alpha desynchronizations emerged for procedural strategies in right frontal, parietal, and temporal regions as function of executive demands. Arithmetic fact retrieval was reflected in right prefrontal increases in theta power. Our results demonstrate differential brain dynamics within frontal-parietal networks across the time course of a problem-solving process, and analyses of different frequency bands allowed us to disentangle cortical regions supporting the underlying memory and executive functions.

The role of physical digit representation and numerical magnitude representation in children’s multiplication fact retrieval

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (Mage=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.

Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study

A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks. We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition. We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand. The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area.

Simple arithmetic: electrophysiological evidence of coactivation and selection of arithmetic facts.

This study aimed at exploring the time course of processes underlying the associative confusion effect. We also evaluated the consequences of selecting arithmetic facts to resolve addition problems. We gathered electrophysiological evidence when participants performed a verification task. Simple addition problems were presented in blocks of two trials and participants decided whether they were correct or not. The N400-like component was considered an index of semantic access (i.e., the retrieval of arithmetic facts), and the P200 component was used to determine the difficulty associated with encoding after the answer to an addition problem. When an addition problem was incorrect but the result presented to the participant was that of multiplying the operands (e.g., 2+4=8), N400-like amplitude was reduced relative to an unrelated condition (e.g., 2+4=10). This finding suggested that the coactivation of addition and multiplication facts took place. Furthermore, the P200 amplitude was more positive when participants answered to addition problems whose result was that of multiplying the operands of the previous trial (e.g., 2+6=8). This suggests that irrelevant results were inhibited and it was difficult to encode them later.

Effects of Prior Knowledge on Memory: Implications for Education

ABSTRACTThe encoding, consolidation, and retrieval of events and facts form the basis for acquiring new skills and knowledge. Prior knowledge can enhance those memory processes considerably and thus foster knowledge acquisition. But prior knowledge can also hinder knowledge acquisition, in particular when the to‐be‐learned information is inconsistent with the presuppositions of the learner. Therefore, taking students' prior knowledge into account and knowing about the way it affects memory processes is important for optimization of students' learning. Recent behavioral and neuroimaging experiments have shed new light on the neural mechanisms through which prior knowledge affects memory. However, relatively little is known about developmental differences in the ability to make efficient use of one's knowledge base for memory purposes. In this article, we review and integrate recent empirical evidence from developmental psychology and cognitive neuroscience about the effects of prior knowledge on memory processes. In particular, this may entail an extended shift from processing in the medial temporal lobes of the brain toward processing in the neocortex. Such findings have implications for students as developing individuals. Therefore, we highlight recent insights from cognitive neuroscience that call for further investigation in educational settings, discussing to what extent these novel insights may inform teaching in the classroom.

A step-by-step tutorial on using the cognitive architecture ACT-R in combination with fMRI data

The cognitive architecture ACT-R is at the same time a psychological theory and a modeling framework for constructing cognitive models that adhere to the principles of the theory. ACT-R can be used in combination with fMRI data in two different ways: (1) fMRI data can be used to evaluate and constrain models in ACT-R by means of predefined Region-of-Interest (ROI) analysis, and (2) predictions from ACT-R models can be used to locate neural correlates of model processes and representations by means of model-based fMRI analysis. In this paper we provide a step-by-step tutorial on both approaches. Note that this tutorial neither teaches the ACT-R theory in any detail, nor fMRI analysis, but explains how ACT-R can be used in combination with fMRI data. To this end, we provide all data and computer code necessary to run the ACT-R model, carry out the analyses, and recreate the figures in the paper. As an example dataset we use a relatively simple algebra task. In the first section, we develop an ACT-R model of this task and fit it to behavioral data. In the second section, we apply a predefined ROI-analysis to evaluate the model using fMRI data. In the third section, we use model-based fMRI analysis to locate the following processes in the brain: retrieval of mathematical facts from memory, working memory updates, motor responses, and visually encoding the problems. After working through this tutorial, the reader will have learned what can be achieved with the two different analysis methods and how they are conducted; the example code can then be adapted to a new dataset.

Are Individual Differences in Arithmetic Fact Retrieval in Children Related to Inhibition?

Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processing. We administered measures of cognitive inhibition (i.e., numerical and non-numerical stroop tasks) and a complementary, more ecologically valid measure of children’s inhibition in the classroom (i.e., teacher questionnaire), as well as numerical magnitude processing (i.e., symbolic and non-symbolic numerical magnitude comparison) and arithmetic fact retrieval (i.e., two verification tasks) in 86 typically developing third graders. We used a correlation, a regression and a Bayesian analysis. This study failed to observe a significant association between inhibition and arithmetic fact retrieval. Consequently, our results did not reveal a unique contribution of inhibition to arithmetic fact retrieval in addition to numerical magnitude processing. On the other hand, symbolic numerical magnitude processing turned out to be a very powerful predictor of arithmetic fact retrieval, as indicated by both frequentist and Bayesian approaches.

Fact learning in complex arithmetic-the role of the angular gyrus revisited.

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Non-symbolic and symbolic notations in simple arithmetic differentially involve intraparietal sulcus and angular gyrus activity

Addition problems can be solved by mentally manipulating quantities for which the bilateral intraparietal sulcus (IPS) is likely recruited, or by retrieving the answer directly from fact memory in which the left angular gyrus (AG) and perisylvian areas may play a role. Mental addition is usually studied with problems presented in the Arabic notation (4+2), and less so with number words (four+two) or dots (:: +·.). In the present study, we investigated how the notation of numbers influences processing during simple mental arithmetic. Twenty-five highly educated participants performed simple arithmetic while their brain activity was recorded with functional magnetic resonance imaging. To reveal the effect of number notation, arithmetic problems were presented in a non-symbolic (Dots) or symbolic (Arabic; Words) notation. Furthermore, we asked whether IPS processing during mental arithmetic is magnitude specific or of a more general, visuospatial nature. To this end, we included perception and manipulation of non-magnitude formats (Colors; unfamiliar Japanese Characters). Increased IPS activity was observed, suggesting magnitude calculations during addition of non-symbolic numbers. In contrast, there was greater activity in the AG and perisylvian areas for symbolic compared to non-symbolic addition, suggesting increased verbal fact retrieval. Furthermore, IPS activity was not specific to processing of numerical magnitude but also present for non-magnitude stimuli that required mental visuospatial processing (Color-mixing; Character-memory measured by a delayed match-to-sample task). Together, our data suggest that simple non-symbolic sums are calculated using visual imagery, whereas answers for simple symbolic sums are retrieved from verbal memory.

ID 314 – Dissociating arithmetic processes in the parietal cortex using repetitive transcranial magnetic stimulation

Numerical cognition involves arithmetic operations which can either be performed by accessing memory of overlearn facts as in the case of multiplications or by performing actual calculations such as in subtraction. Neuropsychological, neuroimaging and brain stimulation methods in both healthy and patient’s studies suggests the involvement of distinct parietal areas in calculations: the horizontal part of the left intraparietal sulcus (hIPS) for multiplication and the left angular gyrus (ANG) for subtraction. However, the anatomical and functional segregation of both processes is not yet fully established. The present study will use a neuronavigation-guided repetitive Transcranial Magnetic Stimulation (rTMS) to induced temporary focal lesion at the left hIPS during a multiplication and subtraction task and at the left ANG while performing the same task. 1 Hz rTMS with 900 continuous pulses and an intensity of 110% active motor threshold will be used in the study. Our hypothesis is that, if the hIPS is specifically critical for retrieval of arithmetic facts then multiplication task performance during and after rTMS will be impaired but not subtraction. Whereas, rTMS to the left ANG will only disrupt subtraction ability but not multiplication.

Behavioural evidence for sex differences in the overlap between subtraction and multiplication.

The present study aims to identify factors that may influence the dissociability of number magnitude processing and arithmetic fact retrieval at the behavioural level. To that end, we assessed both subtraction and multiplication performance in a within-subject approach and evaluated the interdependence of unit-decade integration measures on the one hand as well as sex differences in the interdependence of performance measures on the other hand. We found that subtraction items requiring borrowing (e.g. 53-29 = 24, 3 < 9) are more error prone than subtraction items not requiring borrowing (e.g. 59-23 = 34, 9 > 3), thereby demonstrating a borrowing effect, which has been suggested as a measure of unit-decade integration in subtraction. Furthermore, we observed that multiplication items with decade-consistent distractors (e.g. 6 × 4 = 28 instead of 24) are more error prone that multiplication items with decade-inconsistent distractors (e.g. 6 × 4 = 30 instead of 24), thereby demonstrating a decade-consistency effect, which has been suggested as a measure of unit-decade integration in simple multiplication. However, the borrowing effect in subtraction was not correlated with the effect of decade consistency in simple multiplication in either men or women. This indicates that unit-decade integration arises from different systems in subtraction and multiplication. Nevertheless, men outperformed women not only in subtraction, but also in multiplication. Furthermore, subtraction and multiplication performance on correct solution probes were correlated in women, but unrelated in men. Thus, the view of differential systems for number magnitude processing and arithmetic fact retrieval may not be universal across sexes.

Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children.

Mathematics anxiety (MA) has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations.” Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.

General Mathematical Ability Predicts PASAT Performance in MS Patients: Implications for Clinical Interpretation and Cognitive Reserve.

The Paced Auditory Serial Addition Test (PASAT) is used to assess cognitive status in multiple sclerosis (MS). Although the mathematical demands of the PASAT seem minor (single-digit arithmetic), cognitive psychology research links greater mathematical ability (e.g., algebra, calculus) to more rapid retrieval of single-digit math facts (e.g., 5+6=11). The present study evaluated the hypotheses that (a) mathematical ability is related to PASAT performance and (b) both the relationship between intelligence and PASAT performance as well as the relationship between education and PASAT performance are both mediated by mathematical ability. Forty-five MS patients were assessed using the Wechsler Test of Adult Reading, PASAT and Calculation Subtest of the Woodcock-Johnson-III. Regression based path analysis and bootstrapping were used to compute 95% confidence intervals and test for mediation. Mathematical ability (a) was related to PASAT (β=.61; p<.001) and (b) fully mediated the relationship between Intelligence and PASAT (β=.76; 95% confidence interval (CI95)=.28, 1.45; direct effect of Intelligence, β=.42; CI95=-.39, 1.23) as well as the relationship between Education and PASAT (β=2.43, CI95=.81, 5.16, direct effect of Education, β=.83, CI95=-1.95, 3.61). Mathematical ability represents a source of error in the clinical interpretation of cognitive decline using the PASAT. Domain-specific cognitive reserve is discussed.

Operator priming and generalization of practice in adults' simple arithmetic.

There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication, suggesting that a general addition procedure was primed by the + sign. In Experiment 1 (n = 36), we applied this operator-priming paradigm to rule-based problems (0 + N = N, 1 × N = N, 0 × N = 0) and 1 + N problems with N ranging from 0 to 9. For the rule-based problems, we found both operator-preview facilitation and generalization of practice (e.g., practicing 0 + 3 sped up unpracticed 0 + 8), the latter being a signature of procedure use; however, we also found operator-preview facilitation for 1 + N in the absence of generalization, which implies the 1 + N problems were solved by fact retrieval but nonetheless were facilitated by an operator preview. Thus, the operator preview effect does not discriminate procedure use from fact retrieval. Experiment 2 (n = 36) investigated whether a population with advanced mathematical training-engineering and computer science students-would show generalization of practice for nonrule-based simple addition problems (e.g., 1 + 4, 4 + 7). The 0 + N problems again presented generalization, whereas no nonzero problem type did; but all nonzero problems sped up when the identical problems were retested, as predicted by item-specific fact retrieval. The results pose a strong challenge to the generality of the proposal that skilled adults' simple addition is based on fast procedural algorithms, and instead support a fact-retrieval model of fast addition performance.

From Finding to Explaining

Supporting anomaly analysis in the maritime field is a challenging problem because of the dynamic nature of the task: the definition of abnormal or suspicious behaviour is subject to change and depends on user interests. This paper provides a novel approach to support anomaly analysis in the maritime domain through the exploration of large collections of interpretation reports. Based on observables or more sophisticated patterns, the approach provides information retrieval strategies going from basic facts retrieval that guide short-term corrective actions to more complex networks of related concepts that help domain experts to understand or to explain abnormal vessel behaviours. Semantic integration is used to link various information sources, by using a commonly adopted standard. The paper seeks to explore different aspects of using information retrieval to support the analysis and interpretation of abnormal vessel behaviours for maritime surveillance.

Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study.

Fingers are used as canonical representations for numbers across cultures. In previous imaging studies, it was shown that arithmetic processing activates neural resources that are known to participate in finger movements. Additionally, in one dual-task study, it was shown that anatomically ordered finger tapping disrupts addition and subtraction more than multiplication, possibly due to a long-lasting effect of early finger counting experiences on the neural correlates and organization of addition and subtraction processes. How arithmetic task difficulty and tapping complexity affect the concurrent performance is still unclear. If early finger counting experiences have bearing on the neural correlates of arithmetic in adults, then one would expect anatomically and non-anatomically ordered tapping to have different interference effects, given that finger counting is usually anatomically ordered. To unravel these issues, we studied how (1) arithmetic task difficulty and (2) the complexity of the finger tapping sequence (anatomical vs. non-anatomical ordering) affect concurrent performance and use of key neural circuits using a mixed block/event-related dual-task fMRI design with adult participants. The results suggest that complexity of the tapping sequence modulates interference on addition, and that one-digit addition (fact retrieval), compared to two-digit addition (calculation), is more affected from anatomically ordered tapping. The region-of-interest analysis showed higher left angular gyrus BOLD response for one-digit compared to two-digit addition, and in no-tapping conditions than dual tapping conditions. The results support a specific association between addition fact retrieval and anatomically ordered finger movements in adults, possibly due to finger counting strategies that deploy anatomically ordered finger movements early in the development.

Mathematical abilities in dyslexic children: a diffusion tensor imaging study.

Dyslexia is characterized by a deficit in language processing which mainly affects word decoding and spelling skills. In addition, children with dyslexia also show problems in mathematics. However, for the latter, the underlying structural correlates have not been investigated. Sixteen children with dyslexia (mean age 9.8years [0.39]) and 24 typically developing children (mean age 9.9years [0.29]) group matched for age, gender, IQ, and handedness underwent 3T MR diffusion tensor imaging as well as cognitive testing. Tract-Based Spatial Statistics were performed to correlate behavioral data with diffusion data. Children with dyslexia performed worse than controls in standardized verbal number tasks, such as arithmetic efficiency tests (addition, subtraction, multiplication, division). In contrast, the two groups did not differ in the nonverbal number line task. Arithmetic efficiency, representing the total score of the four arithmetic tasks, multiplication, and division, correlated with diffusion measures in widespread areas of the white matter, including bilateral superior and inferior longitudinal fasciculi in children with dyslexia compared to controls. Children with dyslexia demonstrated lower performance in verbal number tasks but performed similarly to controls in a nonverbal number task. Further, an association between verbal arithmetic efficiency and diffusion measures was demonstrated in widespread areas of the white matter suggesting compensatory mechanisms in children with dyslexia compared to controls. Taken together, poor fact retrieval in children with dyslexia is likely a consequence of deficits in the language system, which not only affects literacy skills but also impacts on arithmetic skills.

Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial–numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities.

Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation.

Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g., 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory (WM). Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial WM also changed with grade. Multiplication correlated with verbal WM and performance in grade 3 but with visuo-spatial WM and performance in grade 4. We suggest that the relation to verbal WM in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic WM in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents.

Effects of Two Interventions on Solving Basic Fact Problems by Second Graders With Mathematics Learning Disabilities

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In addition, the effects of both interventions on students’ fact retrieval performance and generalization performance were also tested. To examine the effects of each intervention, the participants were divided into two groups and the order of the interventions was varied between the two groups. The results showed that, in general, students demonstrated a greater extent of strategy transformation and generalization after receiving the number sense intervention. However, the extensive practice intervention promoted students’ use of retrieval-based strategies to solve basic facts. Findings suggested that both interventions had positive impacts on students with MLD and should be used in tandem.