Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom

In this action research of my 6th grade math class, I investigated whether or not my students would improve their ability to reflect on their learning process when they received descriptive feedback from a peer. I discovered the process of giving and receiving feedback was challenging for the students to initially learn, but eventually using the feedback was highly beneficial. Descriptive feedback allowed the students to learn and understand their mistakes immediately, which in turn improved their learning. In my action research, I also began to discover more ways to implement descriptive feedback in my instruction so it could be more effectively for the students and efficiently so there would be less time taken out from instruction. As a result of this research, I plan to continue having students provide and receive descriptive feedback and to find more evidence of how descriptive feedback could influence student achievement.

Meaningful Independent Practice in Mathematics

In this action research of my seventh grade mathematics classroom, I investigated how students’ explanations of math homework would improve their learning in math. I discovered these explanations can be very beneficial in helping students to improve their understanding of current skills although it did not affect all students. As a result of this study, I plan to incorporate these student explanations in my instruction next year but not as a daily expectation.

Content and English Language Integrated Learning: The use of Moodle in Aircraft Maintenance Training Programs

The aim of this work is to develop a prototype of an e-learning environment that can foster Content and Language Integrated Learning (CLIL) for students enrolled in an aircraft maintenance training program, which allows them to obtain a license valid in all EU member states. Background research is conducted to retrace the evolution of the field of educational technology, analyzing different learning theories – behaviorism, cognitivism, and (socio-)constructivism – and reflecting on how technology and its use in educational contexts has changed over time. Particular attention is given to technologies that have been used and proved effective in Computer Assisted Language Learning (CALL). Based on the background research and on students’ learning objectives, i.e. learning highly specialized contents and aeronautical technical English, a bilingual approach is chosen, three main tools are identified – a hypertextbook, an exercise creation activity, and a discussion forum – and the learning management system Moodle is chosen as delivery medium. The hypertextbook is based on the technical textbook written in English students already use. In order to foster text comprehension, the hypertextbook is enriched by hyperlinks and tooltips. Hyperlinks redirect students to webpages containing additional information both in English and in Italian, while tooltips show Italian equivalents of English technical terms. The exercise creation activity and the discussion forum foster interaction and collaboration among students, according to socio-constructivist principles. In the exercise creation activity, students collaboratively create a workbook, which allow them to deeply analyze and master the contents of the hypertextbook and at the same time create a learning tool that can help them, as well as future students, to enhance learning. In the discussion forum students can discuss their individual issues, content-related, English-related or e-learning environment-related, helping one other and offering instructors suggestions on how to improve both the hypertextbook and the workbook based on their needs.

Next-state comfort in learning a vertical stick transportation sequence

Over the last decade, the end-state comfort effect (e.g., Rosenbaum et al., 2006) has received a considerable amount of attention. However, some of the underlying mechanisms are still to be investigated, amongst others, how sequential planning affects end-state comfort and how this effect develops over learning. In a two-step sequencing task, e.g., postural comfort can be planned on the intermediate position (next state) or on the actual end position (final state). It might be hypothesized that, in initial acquisition, next state’s comfort is crucial for action planning but that, in the course of learning, final state’s comfort is taken more and more into account. To test this hypothesis, a variant of Rosenbaum’s vertical stick transportation task was used. Participants (N = 16, right-handed) received extensive practice on a two-step transportation task (10,000 trials over 12 sessions). From the initial position on the middle stair of a staircase in front of the participant, the stick had to be transported either 20 cm upwards and then 40 cm downwards or 20 cm downwards and then 40 cm upwards (N = 8 per subgroup). Participants were supposed to produce fluid movements without changing grasp. In the pre- and posttest, participants were tested on both two-step sequencing tasks as well as on 20 cm single-step upwards and downwards movements (10 trials per condition). For the test trials, grasp height was calculated kinematographically. In the pretest, large end/next/final-state comfort effects for single-step transportation tasks and large next-state comfort effects for sequenced tasks were found. However, no change in grasp height from pre- to posttest could be revealed. Results show that, in vertical stick transportation sequences, the final state is not taken into account when planning grasp height. Instead, action planning seems to be solely based on aspects of the next action goal that is to be reached.

Spatio-temporal credit assignment in population learning

Learning by reinforcement is important in shaping animal behavior, and in particular in behavioral decision making. Such decision making is likely to involve the integration of many synaptic events in space and time. However, using a single reinforcement signal to modulate synaptic plasticity, as suggested in classical reinforcement learning algorithms, a twofold problem arises. Different synapses will have contributed differently to the behavioral decision, and even for one and the same synapse, releases at different times may have had different effects. Here we present a plasticity rule which solves this spatio-temporal credit assignment problem in a population of spiking neurons. The learning rule is spike-time dependent and maximizes the expected reward by following its stochastic gradient. Synaptic plasticity is modulated not only by the reward, but also by a population feedback signal. While this additional signal solves the spatial component of the problem, the temporal one is solved by means of synaptic eligibility traces. In contrast to temporal difference (TD) based approaches to reinforcement learning, our rule is explicit with regard to the assumed biophysical mechanisms. Neurotransmitter concentrations determine plasticity and learning occurs fully online. Further, it works even if the task to be learned is non-Markovian, i.e. when reinforcement is not determined by the current state of the system but may also depend on past events. The performance of the model is assessed by studying three non-Markovian tasks. In the first task, the reward is delayed beyond the last action with non-related stimuli and actions appearing in between. The second task involves an action sequence which is itself extended in time and reward is only delivered at the last action, as it is the case in any type of board-game. The third task is the inspection game that has been studied in neuroeconomics, where an inspector tries to prevent a worker from shirking. Applying our algorithm to this game yields a learning behavior which is consistent with behavioral data from humans and monkeys, revealing themselves properties of a mixed Nash equilibrium. The examples show that our neuronal implementation of reward based learning copes with delayed and stochastic reward delivery, and also with the learning of mixed strategies in two-opponent games.

Spatio-temporal credit assignment in population learning

Learning by reinforcement is important in shaping animal behavior. But behavioral decision making is likely to involve the integration of many synaptic events in space and time. So in using a single reinforcement signal to modulate synaptic plasticity a twofold problem arises. Different synapses will have contributed differently to the behavioral decision and, even for one and the same synapse, releases at different times may have had different effects. Here we present a plasticity rule which solves this spatio-temporal credit assignment problem in a population of spiking neurons. The learning rule is spike time dependent and maximizes the expected reward by following its stochastic gradient. Synaptic plasticity is modulated not only by the reward but by a population feedback signal as well. While this additional signal solves the spatial component of the problem, the temporal one is solved by means of synaptic eligibility traces. In contrast to temporal difference based approaches to reinforcement learning, our rule is explicit with regard to the assumed biophysical mechanisms. Neurotransmitter concentrations determine plasticity and learning occurs fully online. Further, it works even if the task to be learned is non-Markovian, i.e. when reinforcement is not determined by the current state of the system but may also depend on past events. The performance of the model is assessed by studying three non-Markovian tasks. In the first task the reward is delayed beyond the last action with non-related stimuli and actions appearing in between. The second one involves an action sequence which is itself extended in time and reward is only delivered at the last action, as is the case in any type of board-game. The third is the inspection game that has been studied in neuroeconomics. It only has a mixed Nash equilibrium and exemplifies that the model also copes with stochastic reward delivery and the learning of mixed strategies.

Spatio-temporal credit assignment in population learning

We present a model for plasticity induction in reinforcement learning which is based on a cascade of synaptic memory traces. In the cascade of these so called eligibility traces presynaptic input is first corre lated with postsynaptic events, next with the behavioral decisions and finally with the external reinforcement. A population of leaky integrate and fire neurons endowed with this plasticity scheme is studied by simulation on different tasks. For operant co nditioning with delayed reinforcement, learning succeeds even when the delay is so large that the delivered reward reflects the appropriateness, not of the immediately preceeding response, but of a decision made earlier on in the stimulus - decision sequence . So the proposed model does not rely on the temporal contiguity between decision and pertinent reward and thus provides a viable means of addressing the temporal credit assignment problem. In the same task, learning speeds up with increasing population si ze, showing that the plasticity cascade simultaneously addresses the spatial problem of assigning credit to the different population neurons. Simulations on other task such as sequential decision making serve to highlight the robustness of the proposed sch eme and, further, contrast its performance to that of temporal difference based approaches to reinforcement learning.

Spatio-Temporal Credit Assignment in Neuronal Population Learning

n learning from trial and error, animals need to relate behavioral decisions to environmental reinforcement even though it may be difficult to assign credit to a particular decision when outcomes are uncertain or subject to delays. When considering the biophysical basis of learning, the credit-assignment problem is compounded because the behavioral decisions themselves result from the spatio-temporal aggregation of many synaptic releases. We present a model of plasticity induction for reinforcement learning in a population of leaky integrate and fire neurons which is based on a cascade of synaptic memory traces. Each synaptic cascade correlates presynaptic input first with postsynaptic events, next with the behavioral decisions and finally with external reinforcement. For operant conditioning, learning succeeds even when reinforcement is delivered with a delay so large that temporal contiguity between decision and pertinent reward is lost due to intervening decisions which are themselves subject to delayed reinforcement. This shows that the model provides a viable mechanism for temporal credit assignment. Further, learning speeds up with increasing population size, so the plasticity cascade simultaneously addresses the spatial problem of assigning credit to synapses in different population neurons. Simulations on other tasks, such as sequential decision making, serve to contrast the performance of the proposed scheme to that of temporal difference-based learning. We argue that, due to their comparative robustness, synaptic plasticity cascades are attractive basic models of reinforcement learning in the brain.

Dopamine-related deficit in reward learning after catecholamine depletion in unmedicated, remitted subjects with bulimia nervosa

Disturbances in reward processing have been implicated in bulimia nervosa (BN). Abnormalities in processing reward-related stimuli might be linked to dysfunctions of the catecholaminergic neurotransmitter system, but findings have been inconclusive. A powerful way to investigate the relationship between catecholaminergic function and behavior is to examine behavioral changes in response to experimental catecholamine depletion (CD). The purpose of this study was to uncover putative catecholaminergic dysfunction in remitted subjects with BN who performed a reinforcement-learning task after CD. CD was achieved by oral alpha-methyl-para-tyrosine (AMPT) in 19 unmedicated female subjects with remitted BN (rBN) and 28 demographically matched healthy female controls (HC). Sham depletion administered identical capsules containing diphenhydramine. The study design consisted of a randomized, double-blind, placebo-controlled crossover, single-site experimental trial. The main outcome measures were reward learning in a probabilistic reward task analyzed using signal-detection theory. Secondary outcome measures included self-report assessments, including the Eating Disorder Examination-Questionnaire. Relative to healthy controls, rBN subjects were characterized by blunted reward learning in the AMPT-but not in placebo-condition. Highlighting the specificity of these findings, groups did not differ in their ability to perceptually distinguish between stimuli. Increased CD-induced anhedonic (but not eating disorder) symptoms were associated with a reduced response bias toward a more frequently rewarded stimulus. In conclusion, under CD, rBN subjects showed reduced reward learning compared with healthy control subjects. These deficits uncover disturbance of the central reward processing systems in rBN related to altered brain catecholamine levels, which might reflect a trait-like deficit increasing vulnerability to BN.

The free radical scavenger alpha-phenyl-tert-butyl nitrone aggravates hippocampal apoptosis and learning deficits in experimental pneumococcal meningitis

The effect of adjuvant therapy with the radical scavenger alpha-phenyl-tert-butyl nitrone (PBN; 100 mg/kg given intraperitoneally every 8 h for 5 days) on brain injury and learning function was evaluated in an infant rat model of pneumococcal meningitis. Meningitis led to cortical necrotic injury (median, 3.97% [range, 0%-38.9%] of the cortex), which was reduced to a median of 0% (range, 0%-30.9%) of the cortex (P<.001) by PBN. However, neuronal apoptosis in the hippocampal dentate gyrus was increased by PBN, compared with that by saline (median score, 1.15 [range, 0.04-1.73] vs. 0.31 [range, 0-0.92]; P<.001). Learning function 3 weeks after cured infection, as assessed by the Morris water maze, was decreased, compared with that in uninfected control animals (P<.001). Parallel to the increase in hippocampal apoptosis, PBN further impaired learning in infected animals, compared with that in saline-treated animals (P<.02). These results contrast with those of an earlier study, in which PBN reduced cortical and hippocampal neuronal injury in group B streptococcal meningitis. Thus, in pneumococcal meningitis, antioxidant therapy with PBN aggravates hippocampal injury and learning deficits.

Comparison of the effects of inquiry-based cooperative learning and demonstrations in science education

The reported research project involved studying how teaching science using demonstrations, inquiry-based cooperative learning groups, or a combination of the two methods affected sixth grade students’ understanding of air pressure and density. Three different groups of students were each taught the two units using different teaching methods. Group one learned about the topics through both demonstrations and inquirybased cooperative learning, whereas group two only viewed demonstrations, and group three only participated in inquiry-based learning in cooperative learning groups. The study was designed to answer the following two questions: 1. Which teaching strategy works best for supporting student understanding of air pressure and density: demonstrations, inquirybased labs in cooperative learning groups, or a combination of the two? 2. And what effect does the time spent engaging in a particular learning experience (demonstrations or labs) have on student learning? Overall, the data did not provide sufficient evidence that one method of learning was more effective than the others. The results also suggested that spending more time on a unit does not necessarily equate to a better understanding of the concepts by the students. Implications for science instruction are discussed.