Evaluating the impact of short educational videos on the cortical networks for mathematics

Significance

Teaching mathematical concepts is difficult. To facilitate the comprehension and appeal of mathematics, several teaching websites provide vivid videos illustrating math concepts. Here, however, we show that merely watching such videos fails to improve the brain networks for mathematics. During the video itself, these networks are transiently engaged—but a few minutes later, when we ask questions about the taught concepts, performance is only minimally improved, and the participants engage generic regions thought to be involved in short-term memory and language, rather than the targeted math-responsive regions. Brief video watching is therefore insufficient as a pedagogical device, probably because it misses ingredients such as teacher–pupil interactions, explicit teaching, active engagement, retrieval practice, repetition, and sleep.

Abstract

Many teaching websites, such as the Khan Academy, propose vivid videos illustrating a mathematical concept. Using functional magnetic resonance imaging, we asked whether watching such a video suffices to rapidly change the brain networks for mathematical knowledge. We capitalized on the finding that, when judging the truth of short spoken statements, distinct semantic regions activate depending on whether the statements bear on mathematical knowledge or on other domains of semantic knowledge. Here, participants answered such questions before and after watching a lively 5-min video, which taught them the rudiments of a new domain. During the video, a distinct math-responsive network, comprising anterior intraparietal and inferior temporal nodes, showed intersubject synchrony when viewing mathematics course rather than control courses in biology or law. However, this experience led to minimal subsequent changes in the activity of those domain-specific areas when answering questions on the same topics a few minutes later. All taught facts, whether mathematical or not, led to domain-general repetition enhancement, particularly prominent in the cuneus, posterior cingulate, and posterior parietal cortices. We conclude that short videos do not suffice to induce a meaningful lasting change in the brain’s math-responsive network, but merely engage domain-general regions possibly involved in episodic short-term memory.

Over the past decade, new modes of education have appeared. Massive on-line courses, educational video channels, computer-based gamified educational content, and other open online resources have simplified access to education for a large population. However, creating such digital education tools is not sufficient: their pedagogical impact must also be evaluated. The tools of cognitive neuroscience may help to formally evaluate them, in education settings as well as in lab settings (1). While previous studies have mostly used randomized control trials to evaluate the amount of behavioral improvement compared to a classical pedagogical method (e.g., refs. 2–6), here we show how functional MRI (fMRI) can be used to track the brain mechanisms of such improvement.

In a pedagogical context, behavioral improvement is arguably the only thing that matters. However, neuroimaging can provide complementary insights about the underlying brain mechanisms and may sometimes strongly qualify the observed behavioral progress. For example, Yoncheva et al. (7) showed that, when adults learned to read a new alphabet using either a whole-word or a letter-based attentional focus, behavioral performance for the trained materials improved similarly in both groups, but the underlying change in brain activity was radically different: whole-word training lead to a right-hemispheric bias toward inappropriate circuits distant from the normal left-hemisphere regions for language and reading. In a similar vein, Delazer et al. (8) showed that learning a new arithmetic operation by drill versus by strategy elicits different brain activity in young adults. Functional MRI is now readily accessible to school-age children and college students, and has been used to track the fast brain changes underlying the acquisition of reading (9, 10) or arithmetic (11), as well as to evaluate the brain mechanisms underlying the superior performance of teaching strategies such as retrieval practice and creative mathematical reasoning (12).

While these studies mostly concentrate on skill acquisition, an even more relevant question from a pedagogical standpoint, indeed one of the most difficult and least understood ones, is how to teach the comprehension of a new domain. In the present study, we make one step in this direction by evaluating the neural correlates underlying the acquisition of curricular knowledge in mathematics and in nonmathematical domains. Neuroscience can now start investigating this issue thanks to advances in mapping the distributed brain networks underlying semantic knowledge (13–16). Different types of knowledge, for instance about actions, people, places, animals, or objects, appear to be broadly distributed in partially dissociable brain regions (16–19). In particular, mathematical knowledge, including but not restricted to the knowledge of numbers, can be dissociated from other forms of knowledge (20–22) and relies on a set of regions that respond more to mathematical statements than to other well-matched nonmathematical statements, for instance in geography or history (23–26). In particular, the intraparietal sulcus of both hemispheres, which has long been implicated in mental arithmetic (27, 28) and its acquisition (11, 29), is partially tuned to specific numbers (30–33) but also responds to more abstract mathematical concepts in professional mathematicians (24). So does the more recently discovered posterior inferior temporal gyrus, which was first thought to process the visual form of Arabic numerals (34), but in fact responds bilaterally during mental arithmetic and abstract math (24, 25, 35). Finally, large sectors of lateral prefrontal cortex, dorsal to language-related activations, are also activated by numbers and other math concepts (13, 14, 23–25).

By comparing expert mathematicians versus professors of other disciplines, our previous study suggested that this “math-responsive network” is capable of integrating additional mathematical knowledge (24). When listening to the very same statements, only expert mathematicians activated the math-responsive network when asked to determine the truth value of statements related to abstract math concepts that they had mastered for many years, and showed additional activity when the statements were meaningful rather than meaningless. Thus, the experts managed to integrate, within the same set of areas already engaged in arithmetic in all humans, additional mathematical knowledge.

Here, we capitalize on these findings to ask whether we could visualize the rapid integration of new concepts to the math-responsive network. In the course of learning, a statement which is initially meaningless, because it involves unknown concepts, should become meaningful once those concepts are learned, and should join its appropriate place within the brain’s semantic networks, depending on the category of knowledge involved.

During an fMRI exam, we used four 5-min pedagogical videos to teach new concepts to 21 freshmen math students from Parisian universities. Two of the videos introduced math topics that are typically introduced only much later, during the senior year (measure theory and stochastic processes). Two other videos served as controls and introduced nonmath concepts (plant biology and property law). Learning was assessed by pre- and posttests conducted inside the fMRI. In these tests, participants were asked to judge, as fast as they could, the veracity of spoken math and nonmath statements (Fig. 1). Half of the statements directly probed participants’ understanding of the newly taught concepts, while the other half bore upon either already known notions (taught during high school), or completely unknown notions (untaught). Thus, the design was a 2 × 2 × 3 factorial design with factors of domain (math versus control), time point (pre versus post video training), and content (known, taught, or untaught statements) (see Fig. 1 and Methods for details).

Fig. 1.

Protocol and behavioral results. (A) The fMRI experiment comprised two sessions, each composed of a pretest, a math, and a control video lesson in random order, and a posttest. (B) Structure of the pre- and posttest runs: 40 statements were presented orally, each followed by a short response period and rest period. The table shows examples of statements for each category: math/control × known/taught/untaught. (C) Structure of the video lessons: each lesson comprised five 1-min video sequences, each followed by a rapid introspective evaluation of the participant’s comprehension level. (D) Evolution of performance from pretests to posttests, as assessed by error rates (Left) and mean response times (Right). Error bars indicate one-SEM. Stars indicate the significance level of the difference between pre- and posttests.

We had three main predictions: 1) For known facts, the contrast between math versus control statements should replicate earlier findings on the existence of a math-responsive network (23–26); 2) Repeating those known statements a second time should lead to repetition suppression, a reduction in fMRI signals in the relevant areas; but repeating the unknown statements after the corresponding concepts were taught in the video should, on the contrary, lead to repetition enhancement (36–38). The location of this increase in fMRI signal, which should occur for taught but not for untaught concepts, should indicate which brain circuits are responsible for acquiring this new knowledge. If short videos are pedagogically efficient, taught statements should yield repetition enhancement in their respective math-responsive versus general-knowledge circuits. 3) During the educational videos themselves, fMRI signals should exhibit intersubject correlations (ISC) (39–41), again targeting the relevant semantic networks. The magnitude of such intersubject synchrony may be a marker of the amount of learning, as measured by both behavior and fMRI.

Results

Behavioral Learning Effect.

We first verified that, in the pretests, participants responded way above chance with known statements (chance = 50%; math: 21 ± 9.1% errors in 1.3 ± 0.13 s; control: 22 ± 9.3% errors in 1.1 ± 0.12 s; both p_er < 10⁻⁶, FDR corrected for multiple comparison)(42). Participants were at chance with all the other statements (math taught: 52 ± 11% errors in 1.3 ± 0.11 s; math untaught: 48 ± 11% errors in 1.3 ± 0.12 s; control taught: 51 ± 11% errors in 1.3 ± 0.11 s; control untaught: 51 ± 11% errors in 1.3 ± 0.11 s; all p_er > 0.47) (Fig. 1). Significant differences between the known, taught, and untaught conditions indicated that participants made significantly fewer errors when judging the truth value of known statements (F(2, 40) = 53.4, P < 10⁻¹¹) and also responded faster (F(2, 40) = 4.65, P = 0.015).

After watching the videos, performance improved on statements related to the taught concepts (math: −8.15% errors relative to pretest, P = 0.045; control: −16.5% errors, P < 0.001; all P's FDR corrected for multiple comparisons; Fig. 1D), while responding only slightly and nonsignificantly slower. As expected, no such change was observed for untaught statements (math: −4.94% errors, 0.031 s slower; p_er = 0.11, p_rt = 0.98; control: +0.91% errors, 0.17 s faster; p_er = 0.58, p_rt < 0.01). For previously known statements, performance improved slightly, reflecting the repetition of the same questions (math: −6.24% errors, 0.44 s faster; p_er = 0.043, p_rt < 10⁻⁷; control: −6.88% errors, −0.28 s faster; p_er = 0.001, p_rt < 10⁻⁵). Thus, a 5-min video lesson sufficed to improve performance in both math and control domains, although it is important to note that performance still remained vastly inferior to the performance for previously known statements (Fig. 1D).

During the videos, once per minute, participants rated their comprehension on a 1 to 4 scale. When transformed to a 0 to 100 scale, average comprehension reached 69.7% in math and 72.3% in control videos, a nonsignificant difference (t(20) = 0.93). There was a positive correlation, across participants, between comprehension ratings and performance improvement (math: r = 0.26; control: r = 0.50), though this effect reached significance only for the control statements (P = 0.02).

Math Semantics Is Systematically Processed in a Distinct Set of Brain Regions.

We first tested prediction 1: A different network should be activated by math versus control statements related to known concepts. For this analysis, known statements from both pre- and posttests were pooled. This contrast revealed the classical set of math-responsive brain regions, including bilateral anterior and posterior intraparietal sulci (aIPS and pIPS), bilateral posterior inferior temporal gyri (pITG), bilateral superior frontal gyrus, and the left middle prefrontal gyrus (Fig. 2A and SI Appendix, Table S1), at locations similar to the ones found in our previous research (24, 25). The converse contrast of control versus math known statements showed activity in the left temporal pole and inferior frontal gyrus, bilateral fusiform gyrus, postcentral gyrus, and middle occipital gyrus.

Fig. 2.

Distinct brain networks for mathematical versus general knowledge. Whole-brain inflated maps showing the comparison of activity elicited by (A) known math statements more than known control statements in blue, and the opposite contrast in red; (B) unknown math statements more than unknown control statements in blue, and the opposite contrast in red; (C) known math statements more than unknown math statements in dark blue, and the opposite contrast in cyan; (D) known control statements more than unknown control statements in red, and the opposite contrast in yellow. All maps are thresholded at P < 0.001 uncorrected voxel-wise, and P < 0.05 FDR-corrected cluster-wise. (E) Time course of the BOLD signal for each category of statement in representative brain areas of the network responsive to mathematics: left and right anterior and posterior IPS (aIPS and pIPS), and left and right posterior inferior temporal gyrus (pITG).

We next asked whether the unknown concepts, although unmastered by the participants, were already mapped onto the same differentiated circuits for math versus control concepts, as they partially made use of the same math vocabulary. We thus compared math versus control statements involving unknown concepts (pooling together both taught and untaught concepts in pretests, as well as untaught concepts in posttests). Although the differences were weak, there was a slightly greater activation for math statements compared with control statements mostly in the left hemisphere in the angular gyrus (AG) extending through the inferior parietal lobule (IPL), and in the inferior temporal gyrus (ITG), as well as in the posterior cingulate cortex (PCC) and cuneus along the brain midline (Fig. 2B and SI Appendix, Table S1). While the parietal and inferior temporal sites were close to the math-responsive network, they only partially overlapped.

The direct contrast of known versus unknown math concepts (Fig. 2C) yielded a map similar to the one comparing known math versus control statements, again revealing the classical math-responsive network composed of bilateral aIPS, bilateral pITG, and various middle and superior frontal sites (Fig. 2C and SI Appendix, Table S2). In the converse direction, unknown math concepts induced more activity than known math concepts in the bilateral superior temporal sulcus (STS), the bilateral lingual and middle occipital gyri, the left inferior frontal gyrus, as well as in the PCC and cuneus. These regions are outside of the math-responsive network, and partially overlap with classical areas for spoken or written sentence processing, thus suggesting that sentences comprising unknown words may have induced a greater amount of difficulty within language comprehension networks. Indeed, these results, particularly the greater activation of the bilateral superior temporal regions and lingual areas, were partially replicated when contrasting unknown versus known control concepts (Fig. 2D and SI Appendix, Table S2).

These results are illustrated in Fig. 2E by plots of the average timecourse of the neural response within the six main math-responsive regions revealed by the contrast of math versus control statements (bilateral aIPS, pIPS, and pITG). In those regions, following the auditory presentation of the statement, the BOLD signal systematically rose to known math concepts, and to a much lesser extent to unknown math concepts in both aIPS, but no activation or even a deactivation was seen in all other cases. Taken together, these results suggest that known math statements differed from all other statements in their capacity to strongly activate the math-responsive network (23–26).

Learning Effect due to Exposure to the Videos.

We then evaluated the main goal of our experiment, i.e., whether the learning sessions affected brain activity by channeling the taught math statements toward the math-responsive network. To do so, we compared the neural activity elicited by posttest versus pretest presentations of the same math statements, before and after the relevant concepts were taught. However, this contrast did not reveal the expected math-responsive network. Rather, repetition enhancement was seen in the posterior mesial part of the brain, i.e., in the cuneus/precuneus and PCC accompanied by a large swath of activity in the left posterior inferior parietal cortex/AG, the anterior part of the middle frontal gyrus, and bilateral caudate nuclei (SI Appendix, Table S3).

Importantly, this result was not specific to math. On the contrary, a very similar network including the cuneus/precuneus, PCC, left IPL/AG, middle frontal sites, and bilateral caudate nuclei was observed for the pre- versus post- contrast with taught control statements (SI Appendix, Table S3). Indeed, no region showed a significant interaction (post − pre) × (math − control) for taught concepts.

Because activation could change across time or sentence repetition without implying a learning effect, we replicated the above analysis using two more specific contrasts: C1 = (post − pre) × (taught − untaught), and C2 = (post − pre) × [ taught − (known & untaught)]. The results were similar, consistently revealing activity in the caudate nuclei, left IPL/AG, cuneus/precuneus and middle frontal gyrus (SI Appendix, Table S3). Again, there was no difference between math and control, as no region showed significant interactions C1 × (math − control) or C2 × (math − control). Fig. 3A shows the main effect of repetition enhancement imputable to learning, pooling over both math and control concepts (contrast C2).

Fig. 3.

Effects of learning at the brain level. (A) Interaction effect indicating significantly greater activity during posttests than during pretests, for taught statements more than for known and untaught statements, pooling across math and control statements (voxel-wise P < 0.001 uncorrected, cluster-wise P < 0.05 with FDR correction). Histograms show the mean beta estimates for each category of statements in both pre- and posttests, extracted from the principal clusters of activation. (B) Mean beta estimates for each category of statements in both pre- and posttests (Right), extracted from the six main math-related regions of interest, displayed on an inflated brain (Left).

The histograms of Fig. 3A illustrate the details of these effects. A small amount of repetition enhancement occurred even to known statements in some regions (PCC, cuneus/precuneus, and middle frontal gyrus). However, all regions showed a much larger increase in activation selectively for taught statements after viewing the video. Furthermore, such learning-induced repetition enhancement was identical for math and nonmath, and therefore unselective for contents.

The regions exhibiting an increase in activation after viewing the videos partially overlap with regions involved in episodic memory and language processing, but not within the math-responsive brain network. We further confirmed that the newly taught concepts did not trigger the activation of the math-responsive network thanks to a sensitive analysis using subject-specific voxels within the six main math-related regions-of-interest (Fig. 3B). Voxels were identified using the contrast for simple calculation versus sentence processing from a short localizer completed at the end of the main fMRI experiment. We then conducted an ANOVA with hemisphere, region (aIPS, pIPS, or pITG), content type (math or control nonmath), statement category (know, taught, or untaught), and test phase (pre- or post-) as within-subject factors. We observed generally greater activation in the left hemisphere compared with the right hemisphere (F(1, 19) = 35.1, P < 2.10⁻⁵), for math statements compared with control nonmath statements (F(1, 19) = 29.4, P < 4.10⁻⁵). We also found a main effect of the statement category (F(2, 38) = 7.61, P = 0.002), but no effect of the region of interest (F(2, 38) = 1.97, P = 0.153).

Turning to the analysis of the effect of learning, we found repetition suppression for known math statements (F(1, 19) = 17.4, P < 0.001), no significant difference between pre- and posttests for untaught concepts (F(1, 19) = 0.357, P = 0.557), and a clear repetition enhancement for both taught math and taught control concepts alike (Math: F(1, 19) = 11.6; Control: F(1, 19) = 11.7; both P's < 0.003). Indeed, the interaction (Math − Control) × (Taught − Untaught) × (Pre − Post) was not significant (F(1, 19) = 0.042, P = 0.839). Thus, freshly learned math concepts yielded enhanced activity in the math-responsive brain regions, but in the same proportion as freshly learned control concepts.

Intersubject correlations during Exposure to the Videos.

The above results indicated that a short period of learning was not sufficient to selectively channel the taught math concepts toward the math-responsive network, and instead mobilized the precuneus and related regions not specifically involved in mathematics (Fig. 3). To clarify what happened during the learning process, we investigated participants’ neural responses during the video lessons themselves. Because videos are complex stimuli that involve rich visual and auditory inputs combined in elaborate narratives, we analyzed neural activity during video watching by calculating ISC, a data-driven analysis technique that locates any brain region reliably entrained by the videos in a systematic way across participants.

Fig. 4A shows the comparison of ISC during math versus control videos. Relative to control videos, math videos elicited more synchronous activity among participants in bilateral IPS and right pITG, as well as at various frontal sites of the right hemisphere (SI Appendix, Table S4). The converse contrast revealed synchronous activity along the STS of both hemispheres, in the primary visual cortex, in the bilateral fusiform gyrus, and the left inferior frontal gyrus. Therefore, our videos were partially successful in engaging the appropriate semantic networks, in a distinct manner for math versus control videos, in agreement with previous results on the capacity of brief pedagogical videos to activate those brain systems (39, 43, 44).

Fig. 4.

Analysis of brain activity during the video lessons. (A) Whole-brain inflated maps showing the regions with temporally correlated activation across participants (ISC) during math video lessons more than during control video lessons in blue, and the opposite contrast in red (voxelwise P < 0.001 uncorrected, clusterwise P < 0.05 FDR-corrected). (B) Correlation between the mean ISC value extracted from the six main math-related regions of interest, and the performance increase from pre- to posttests across participants, separately for math (Top Row) and control (Bottom Row). We observed negative correlations between ISC during math video lessons and the performance increase on taught math statements in most regions of interest. In the same regions, there was no significant correlation between ISC during the control nonmath video lessons and the performance increase on taught control statements.

Previous research suggested that children’s neural maturity during video watching, as assessed by the similarity of their activation patterns to those of adults, predicted their performance in arithmetic and letter knowledge (39). Here, we similarly asked whether the similarity of a person’s math-related brain responses to the group, during video watching, reflected the extent to which they learned from it. We thus investigated whether interindividual differences in learning (i.e., performance increase from pre- to posttests) were related to interindividual differences in the strength of neural response correlation, in the math-responsive regions, between each individual and the rest of the group while watching the video lessons.

Contrary to what we expected, we found significant inverse correlations in almost all pre-defined math-related regions of interest (Left aIPS: r = −0.534; Right aIPS: r = −0.448; Left pIPS: r = −0.400; Right pIPS: r = −0.481; Left pITG: r = −0.341; Right pITG: r = −0.541; reaching significance in all regions but both left pIPS and pITG) (Fig. 4B). The higher an individual ISC during the math video lessons, the smaller his or her increase in performance on taught math concepts. No such pattern was found between individual ISC evaluated during the control video lessons and the increase in performance on taught control concepts. Inspired by previous findings (39, 45), we also explored which regions of the brain exhibited a positive correlation between intersubject synchrony and the amount of learning. To do so, the Pearson correlation coefficient between ISC and performance increase was computed across participants in each voxel of the brain, separately for the math and control videos. We found positive correlations in small clusters outside the math-responsive network, particularly in the para-hippocampal gyrus (bilateral for math videos, [−30, −18, −24], r = 0.725, and [18, −16, −24], r = 0.672; right only for control videos, [26, 7, −28], r = 0.656), but none survived a voxel-wise threshold of P < 0.001. These results suggest that, in the present context of short-term video learning, the synchronization of neural responses with the rest of the group, within the math-responsive network, primarily entertains a negative relation to learning.

Discussion

Our goal was to study the impact of a short video lesson on the brain’s semantic networks. To this aim, we scanned participants with fMRI while they answered simple true/false questions on mathematical and nonmathematical topics, before and after being exposed to a 5-min educational video. Learning did occur, as evidenced by changes in both behavioral accuracy and brain activity evoked by statements in the taught domain, but not in previously known or in untaught domains. However, activation did not increase in areas encoding domain-specific semantic knowledge, but only in a domain-general network prominently including the cuneus/precuneus, AG, and bilateral caudate, and indifferently so for math and nonmath statements. We now discuss what these results imply for brain organization, pedagogy, and video-based learning.

Our work was predicated upon the dissociation, reported in several prior studies, between brain regions involved in the representation of mathematical facts and in other domains of knowledge (22–28). It is therefore important that we replicated these observations in two different ways. First, for facts that participants already knew before the experiment, we observed a clear separation between those two sets of regions (Fig. 2A). As in previous work, mathematical statements, compared with control nonmathematical statements induced greater activity in bilateral anterior intraparietal and posterior inferotemporal regions, while control nonmathematical statements induced greater activity in other areas classically involved in high-level semantic integration and memory, notably the bilateral temporal poles (15, 46, 47). The present experiment also included another control, the contrast of known versus unknown facts. Although less diagnostic, perhaps because participants searched their semantic memory when faced with unknown facts, this contrast evidenced a bilateral anterior intraparietal as well as right ventral temporal activation specific to known mathematical facts (Fig. 2C). Those within-subject results in undergraduate math students concur with a prior between-subject comparison of mathematicians versus nonmathematicians (24). Together, they confirm that math-responsive regions, which are systematically involved in encoding numbers and simple arithmetic (30–33), also respond to complex nonnumerical mathematical facts in mathematically educated participants.

A similar conclusion was reached by measuring ISC in brain activity while participants watched pedagogical movies (Fig. 4). During math movies, compared with control nonmath movies, intersubject synchronization was stronger in bilateral anterior intraparietal and right ventral temporal areas, i.e., the same regions that were previously found to be math-responsive and selective for known math facts (compare Figs. 2 and 4). In the converse direction, nonmath movies tended to evoke greater synchrony in a more distributed set of areas, again including left and right anterior temporal regions. In past studies, fMRI intersubject synchrony in naturalistic settings (40, 41, 45) was found useful to evaluate, not only the activation of sensory areas driven by specific stimuli such as faces, but also of more abstract, semantic cortical regions, for instance those shared between movie watching and story listening (48), spoken and written versions of the same story (49), bilingual presentations of the same story (50), or listening to a story versus producing it (51). When people diverged in their comprehension of an ambiguous story, their ISCs reflected which meaning they grasped (48, 52). ISC thus seems well suited to track the comprehension of a pedagogical lesson. Indeed, several recent studies have shown that ISC can track teacher–student dynamics using fMRI (45, 53), functional near-infrared spectroscopy (54) or electro-encephalography (55, 56). Furthermore, previous fMRI studies showed content-selective ISC in children watching educational videos, with intraparietal cortex showing greater ISC during number- and arithmetic- than during letter- and grammar-related video segments (39, 57). The present study confirms this finding: ISC varied with the content of the videos and concentrated in the bilateral intraparietal sulcus and other math-responsive areas during math relative to control lessons (Fig. 4).

Following the video, as predicted, we found repetition enhancement, i.e., an increase in fMRI activity evoked by statements bearing on the learned materials. Thus, our results confirm that repetition enhancement can serve as a marker of learning (36–38). Nevertheless, the impact of such video training on subsequent judgements differed from our predictions in two ways. First, learned statements failed to evoke domain-specific brain networks: no difference was found between taught math versus taught nonmath statements. Second, the regions where learning occurred (as evidenced by larger repetition enhancement for taught concepts than for known or untaught ones)—cuneus, posterior cingulate, caudate, AG, and middle frontal gyrus—failed to be strongly activated by previously known statements (Fig. 3A). Thus, immediately following learning, the learned facts were not yet routed to the relevant content-specific brain areas, and instead, were held in a distinct network. Attributing a function to this set of regions is difficult, given the well-known pitfalls of “reverse inference”, i.e., the difficulty of inferring cognitive processes from brain-imaging data (58, 59). However, we note that part of this network (AG, precuneus, PCC) is active during high-level language processing and participates in a slow semantic integration system which is thought to store the meanings of passages or movies in episodic memory (60, 61) and replay them in imagination (62). Our results concur with a previous study where learning to solve mathematical problems also led to short-term repetition enhancement in the posterior cingulate, precuneus, and retrosplenial cortex as participants repeatedly practiced solving the same problems (37). Together, these observations suggest that, initially, mathematical learning recruits domain-general short-term episodic memory. Participants may have answered the postvideo questions at above-chance level by evoking a rote literal memory of the movies (verbal or visual), without yet reaching a deep understanding of mathematical meaning. Indeed, such a shallow strategy may be the only available one when a student is first introduced, in a few minutes, with several new words and concepts.

The episodic memory interpretation may also shed light on the surprising finding of a negative correlation, across participants, between ISC in the math-responsive network, and the amount of learning. In their study of Sesame Street videos, Cantlon and Li (39) demonstrated that the amount of synchrony with adults in the intraparietal cortex was a positive predictor of math performance. Likewise, Hasson et al. (45) observed that enhanced ISC was a positive predictor of episodic memory 3 wk later. The present conditions are quite different, however, and the negative correlation may be due to the fact that it is essentially impossible to integrate so many new facts into the mathematical semantic network in just 5 min. Therefore, the participants who succeed in answering some of our questions after watching the videos are not those who tried to deeply understand the math, but those who merely stored some of the taught materials using a domain-general episodic memory network. In agreement with this interpretation, we found a trend toward positive correlations across participants between ISC and the amount of learning in the parahippocampal gyrus, i.e., regions similar to those identified by Hasson et al. (45) and linked to episodic memory retrieval (63–66).

While this interpretation is speculative and will require further testing, one conclusion is clear: an entertaining 5-min pedagogical video fails to teach mathematical facts at a deep, domain-specific level. Undoubtedly, short videos may be useful to convey intuitions, visualizations, and enthusiasm for math, but the actual, operational knowledge that they leave in the viewer’s memory is limited. As discussed in the introduction, behavioral evidence of learning can be ambiguous and may be compatible with memory storage in various brain networks. Brain imaging provides a complementary viewpoint by demonstrating whether or not the relevant domain-specific areas are involved (7).

A crucial question for further research is, which pedagogical factors could facilitate students’ shift from shallow domain-general memory to deeper domain-specific semantic networks? The present design provides a general strategy to probe the efficacy of any educational experience, either online or in the classroom, at the brain level. The rich literature on the scientific foundations of learning (67–70) suggests that brief educational videos often lack the key ingredients that facilitate efficient learning, including eye-to-eye teacher–pupil interactions (71), explicit and direct instruction (72), active pupil engagement (12, 73), retrieval practice (74), spaced repetition (75), and sleep-dependent consolidation (76). While the present experiment was limited to a single fMRI session, extending it to a repeated longitudinal design would permit tracking which of these factors favor the optimal integration of abstract mathematical information into the appropriate brain networks.

Materials and Methods

Participants.

Twenty-one math major students, all in their freshman or sophomore year in math, took part in this study (14 male, 7 female, age range 18 to 23, mean = 20). They were recruited in various Parisian universities and preparatory classes. They were included in this experiment based on their answers to a questionnaire insuring that did not already know what was about to be taught but mastered the background knowledge mandatory to understand the lessons.

All participants gave written informed consent and were paid for their participation. The experiment was approved by the regional ethics committee for biomedical research (Comité de Protection des Personnes, Hôpital de Bicêtre).

Procedure.

The fMRI exam was divided into two consecutive sessions. Each session started with a knowledge pretest in which participants were asked to judge as fast as they could whether 40 spoken math and control nonmath statements were true or false. Participants were then presented with one math and one nonmath pedagogical video lessons. The order of video lessons was counterbalanced between the two sessions (session 1: measure theory followed by plant biology; session 2: property law followed by stochastic processes), and the session order was randomly assigned to participants. Each session ended with a knowledge posttest, consisting of the same 40 spoken math and control nonmath statements that were presented during pretest (Fig. 1). After the fMRI exam, participants were asked, without time limit, to give their definitions of the concepts taught by the four video lessons they watched.

Test Runs.

Participants were presented with a total of 40 math statements and 40 control nonmath statements. In each session, five math and five control statements were related to familiar notions extracted from the high school math and French curricula; 10 math and 10 control statements were related to the concepts introduced in the video lessons; five math and five control statements dealt with completely unknown concepts. The 10 math concepts introduced during the fMRI exam were part of the typical senior year math curriculum: measure theory (Sets, Countability, σ-Algebra, Lebesgue measure, and Lebesgue integral) and stochastic processes (Brownian motion, stochastic, Gaussian, and Markov processes, and Hidden Markov Model). The 10 control nonmath concepts introduced in this experiment came from completely unrelated fields that also typically use very specific vocabulary: Property law (legal person, estate, inheritance, usufruct, and annuity) and plant biology (gymnosperm, angiosperm, dicotyledon, spermatophyte, and graminoid).

Within each category of statements (known, taught, and untaught), half were true, and half were false. Reference to numbers or to other mathematical concepts was purposely avoided. A complete list of statements, translated from the original French, is presented in SI Appendix.

All statements were recorded by a female native French speaker who was familiar with mathematical concepts. Statements from the different categories were matched in syntactic construction, length (mean number of syllables: math = 16.9; control = 17.2; t = −0.58, P = 0.56, no significant difference between categories: F(5, 74) = 0.61, P = 0.69), and duration (math = 3.28 s; control = 3.23 s; t = 0.80, P = 0.42, no significant difference between categories: F(5, 74) = 1.25, P = 0.29).

Each session comprised two test runs, one before and one after the presentation of the videos, that both included the same 40 statements presented in random order. On screen, the only display was a fixation cross on a black background. The onset of each statement was announced by a beep and the fixation cross briefly turning to red. After the auditory presentation of a statement, the fixation cross turned to green, signaling that a response was expected. Participants were given 2.5 s to evaluate whether the statement was true or false, by pressing one of two corresponding buttons (held in the right hand). Each trial ended with a 7-s resting period (Fig. 1).

Video Runs.

Each video run consisted of two video lessons separated by a 30-s resting period. Each video lesson was composed of five consecutive 53-s video sequences, each teaching a given concept (SI Appendix, Figs. S1 and S2). In 5 min, we implemented a pedagogical progression that started with an intuitive overview and motivation, then progressively introduced a few key words and concepts of the target domain. The video sequences were created by one of the authors, PR (a mathematics teacher) using the application “Explain Everything”. On a white background, videos presented an attractive combination of pictures, animations, keywords, and auditory explanations, vividly illustrating the relevant concepts. Math and control video sequences were matched in duration (math = 55 s, control = 52 s, t = 1.03, P = 0.32). After each video sequence, participants were given 3 s to report their level of understanding, on a 1 to 4 scale, by pressing one of the four corresponding buttons they held in the right hand. Each sequence ended with a 7-s resting period with a black fixation cross on a white background.

Localizer Run.

This 5-min run is described in detail elsewhere (77), and includes mental processing of simple subtraction problems presented visually or auditorily, contrasted to the processing of written or spoken sentences of equivalent duration and complexity. This contrast was used to select voxels activated by math processing at the individual level.

fMRI Data Acquisition and Analysis.

We used a 3-Tesla whole-body system (Siemens Trio) with a 64-channel head-coil and multiband imaging sequences [multiband factor = 3, Grappa factor = 0, 60 interleaved axial slices, 1.75-mm thickness and 1.75-mm isotropic in-plane resolution, repetition time (RT) = 1,810 ms, echo time (ET) = 30.4 ms].

Using SPM12 software, functional images were first realigned, normalized to the standard Montreal Neurological Institute brain space, resampled to 1.5-mm voxel size, and spatially smoothed with an isotropic Gaussian filter of 2 mm FWHM.

For test runs, a two-level analysis was then implemented in SPM12 software. For each participant, fMRI images were high-pass filtered at 128 s, and time series were modeled by one regressor for each statement (kernel = sentence duration + mean response time). Regressors of noninterest included the six framewise displacement parameters extracted from previous realignment. We defined subject-specific contrasts for each category of statements—Math/Control × Known/Taught/Untaught × Pre-/Posttest—versus rest. These contrasts were then smoothed with an isotropic Gaussian filter of 5 mm FWHM and finally entered in a second-level whole-brain ANOVA with statement conditions as within-subject factors.

For video runs, we used the technique of ISC, which consists in identifying brain regions where the response to a stimulus is correlated among participants (78).

The six framewise displacement parameters were regressed out, and a 100-s high-pass filter was applied. Rest periods at the beginning of each run were then trimmed, resulting in four video runs of 169, 158, 148, and 163 TRs each. Each run was finally z-scored (standardized to zero mean and unit variance) for each voxel. An average gray-matter mask was applied prior to performing any further analyses. The ISC was then calculated using the leave-one-out approach: At each voxel, each subject’s time series (i.e., each run) was correlated with the average time series of all the other participants (78). This approach gave us four R-maps for each participant that were converted into z-maps using the Fischer transformation. At the group level, the z-maps of each task were entered in a repeated measure ANOVA. All brain activation results are reported with an uncorrected voxelwise threshold of P < 0.001, and an FDR-corrected clusterwise threshold of P < 0.05.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Anonymized behavior data have been deposited in OSF (DOI:10.17605/OSF.IO/GA2MH). Some study data available (Restrictions apply to MRI data due to the size of the files) (42).