Solving Arithmetic Mathematical Word Problems: A Review and Recent Advancements

Mandal, Sourav; Naskar, Sudip Kumar

doi:10.1007/978-981-10-7590-2_7

Cited by 20 publications

(8 citation statements)

References 16 publications

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“…Each condition consisted of 35 instances. Both of the abovementioned datasets have been widely used in previous machine learning studies on MW problems (Mandal & Naskar, 2019). For our MW conditions, the original English sentences were translated into Japanese by the first author (T.N.).…”

Section: Methodsmentioning

confidence: 99%

Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

Nakai

Nishimoto

2023

Eur J of Neuroscience

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Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel‐wise encoding models. Both intra‐ and cross‐format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format‐invariant manner.

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Section: Methodsmentioning

confidence: 99%

Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

Nakai

Nishimoto

2023

Eur J of Neuroscience

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“…In this section, we evaluate the effectiveness of the proposed model on math problems from the widely used benchmark MAWPS. MAWPS [ 36 , 37 ] is an online repository of Math Word Problems and provides a unified test-bed to evaluate different algorithms. MAWPS allows for the automatic construction of datasets with particular characteristics, providing tools for tuning the lexical and template overlap of a dataset as well as for filtering ungrammatical problems from web-sourced corpora.…”

Section: Methodsmentioning

confidence: 99%

An Improved Math Word Problem (MWP) Model Using Unified Pretrained Language Model (UniLM) for Pretraining

Zhang

2022

Computational Intelligence and Neuroscience

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Natural Language Understanding (NLU) and Natural Language Generation (NLG) are the general methods that support machine understanding of text content. They play a very important role in the text information processing system including recommendation and question and answer systems. There are many researches in the field of NLU such as Bag of words, N-Gram, and neural network language model. These models have achieved a good performance in NLU and NLG tasks. However, since they require lots of training data, it is difficult to obtain rich data in practical applications. Thus, pretraining becomes important. This paper proposes a semisupervised way to deal with math word problem (MWP) tasks using unsupervised pretraining and supervised tuning methods, which are based on the Unified pretrained Language Model (UniLM). The proposed model requires fewer training data than traditional models since it uses model parameters of tasks that have been learned before to initialize the model parameters of new tasks. In this way, old knowledge helps new models successfully perform new tasks from old experiences instead of from scratch. Moreover, in order to help the decoder make accurate predictions, we combine the advantages of AR and AE language models to support one-way, sequence-to-sequence, and two-way predictions. Experiments, carried out on MWP tasks with 20,000+ mathematical questions, show that the improved model outperforms the traditional models with a maximum accuracy of 79.57%. The impact of different experiment parameters is also studied in the paper and we found that a wrong arithmetic order leads to incorrect solution expression generation.

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“…Each condition consisted of 35 instances. Both of the abovementioned datasets have been widely used in previous machine learning studies on MW problems (Mandal & Naskar, 2019). For our MW problems, the original English sentences were translated into Japanese by the first author (T.N.).…”

Section: Stimuli and Testing Proceduresmentioning

confidence: 99%

Quantitative modeling demonstrates format-invariant representations of mathematical problems in the brain

Nakai

Nishimoto

2022

Preprint

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Mathematical thoughts can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modeling of mathematical problem solving has yet to be attempted. In the present study, eight subjects were subjected to 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra-and cross-format encoding modeling significantly predicted brain activity in the bilateral intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the bilateral IPS. These findings support the idea that our mathematical thoughts are represented in the brain in a format-invariant manner.

show abstract

Solving Arithmetic Mathematical Word Problems: A Review and Recent Advancements

Cited by 20 publications

References 16 publications

Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

An Improved Math Word Problem (MWP) Model Using Unified Pretrained Language Model (UniLM) for Pretraining

Quantitative modeling demonstrates format-invariant representations of mathematical problems in the brain

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