Abstract Due to the importance of textbooks within the processes of teaching and learning in Mathematics, this article focuses on the tasks proposed in five textbooks of 1st of Bachillerato for this topic. The goal is to identify meanings of derivative in the textbooks through the proposed tasks. It is a quantitative research in which, by means of a cluster analysis, the tasks were grouped according to similarity. The results show that the books emphasize three meanings of the derivative: one procedural-algebraic, one algorithmic, and finally another conceptual-geometric meaning, all of them dominated by the symbolic representation system and that exclusively show a mathematical context.

Data from a comparative judgement survey consisting of 62 working mathematics educators (ME) at Norwegian universities or city colleges, and 57 working mathematicians at Norwegian universities. A total of 3607 comparisons of which 1780 comparisons by the ME and 1827 ME. The comparative judgement survey consisted of respondents comparing pairs of statements on mathematical definitions compiled from a literature review on mathematical definitions in the mathematics education literature. Each WM was asked to judge 40 pairs of statements with the following question: “As a researcher in mathematics, where your target group is other mathematicians, what is more important about mathematical definitions?” Each ME was asked to judge 41 pairs of statements with the following question: “For a mathematical definition in the context of teaching and learning, what is more important?” The comparative judgement was done with No More Marking software (nomoremarking.com) The data set consists of the following data: comparisons made by ME (ME.csv) comparisons made by WM (WM.csv) Look up table of codes of statements and statement formulations (key.csv) Each line in the comparison represents a comparison, where the "winner" column represents the winner and the "loser" column the loser of the comparison.

Abstract In this paper we turn our attention to the different language games associated to the development of Mathematical Modelling activities and to the meanings constituted by students within these language games in relation to the first order ordinary differential equations. The research is based on Mathematical Modelling in Mathematics Education and has as its philosophical basis the studies of Ludwig Wittgenstein and some of his interpreters. Considering these theoretical-philosophical elements, mathematical modelling activities were developed in a Mathematics Degree in a course of Ordinary Differential Equations. Data were collected through written records, audio and video recordings, questionnaires, and interviews. The data analysis methodology considers the students' discursive practices and allowed us to construct trees of idea association. The results indicate that the constitution of meaning within modelling activities is associated to the students' linguistic appropriation of the rules and techniques that are configured in specific language games identified in the Mathematical Modelling activities.

GSM8K - Grade School Math 8K Q&A

A Linguistically Diverse Dataset for Multi-Step Reasoning Question Answering

By Huggingface Hub [source]

About this dataset

This Grade School Math 8K Linguistically Diverse Training & Test Set is designed to help you develop and improve your understanding of multi-step reasoning question answering. The dataset contains three separate data files: the socratic_test.csv, main_test.csv, and main_train.csv, each containing a set of questions and answers related to grade school math that consists of multiple steps. Each file contains the same columns: question, answer. The questions contained in this dataset are thoughtfully crafted to lead you through the reasoning journey for arriving at the correct answer each time, allowing you immense opportunities for learning through practice. With over 8 thousand entries for both training and testing purposes in this GSM8K dataset, it takes advanced multi-step reasoning skills to ace these questions! Deepen your knowledge today and master any challenge with ease using this amazing GSM8K set!

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How to use the dataset

This dataset provides a unique opportunity to study multi-step reasoning for question answering. The GSM8K Linguistically Diverse Training & Test Set consists of 8,000 questions and answers that have been created to simulate real-world scenarios in grade school mathematics. Each question is paired with one answer based on a comprehensive test set. The questions cover topics such as algebra, arithmetic, probability and more.

The dataset consists of two files: main_train.csv and main_test.csv; the former contains questions and answers specifically related to grade school math while the latter includes multi-step reasoning tests for each category of the Ontario Math Curriculum (OMC). In addition, it has three columns - Question (Question), Answer ([Answer]) – meaning that each row contains 3 sequential question/answer pairs making it possible to take a single path from the start of any given answer or branch out from there according to the logic construction required by each respective problem scenario; these columns can be used in combination with text analysis algorithms like ELMo or BERT to explore different formats of representation for responding accurately during natural language processing tasks such as Q&A or building predictive models for numerical data applications like measuring classifying resource efficiency initiatives or forecasting sales volumes in retail platforms..

To use this dataset efficiently you should first get familiar with its structure by reading through its documentation so you are aware all available info regarding items content definition & format requirements then study examples that best suits your specific purpose whether is performing an experiment inspired by education research needs, generate insights related marketing analytics reports making predictions over artificial intelligence project capacity improvements optimization gains etcetera having full access knowledge about available source keeps you up & running from preliminary background work toward knowledge mining endeavor completion success Support User success qualitative exploration sessions make sure learn all variables definitions employed heterogeneous tools before continue Research journey starts experienced Researchers come prepared valuable resource items employed go beyond discovery false alarm halt advancement flow focus unprocessed raw values instead ensure clear cutting vision behind objectives support UserHelp plans going mean project meaningful campaign deliverables production planning safety milestones dovetail short deliveries enable design interfaces session workforce making everything automated fun entry functioning final transformation awaited offshoot Goals outcome parameters monitor life cycle management ensures ongoing projects feedbacks monitored video enactment resources tapped Proficiently balanced activity sheets tracking activities progress deliberation points evaluation radius highlights outputs primary phase visit egress collaboration agendas Client cumulative returns records capture performance illustrated collectively diarized successive setup sweetens conditions researched environments overview debriefing arcane matters turn acquaintances esteemed directives social

Research Ideas

• Training language models for improving accuracy in natural language processing applications such as question answering or dialogue systems.
• Generating new grade school math questions and answers using g...

Protein-Protein, Genetic, and Chemical Interactions for MATH-4 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: Protein MATH-4

Protein-Protein, Genetic, and Chemical Interactions for MATH-50 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: math-50 encodes a protein which has a meprin-associated Traf homology (MATH) domain and may be involved in apoptosis.

Protein-Protein, Genetic, and Chemical Interactions for MATH-48 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: MATH (meprin-associated Traf homology) domain containing

A new approach to the validation of surface texture form removal methods is introduced. A linear algebra technique is presented that obtains total least squares (TLS) model fits for a continuous mathematical surface definition. This model is applicable to both profile and areal form removal, and can be used for a range of form removal models including polynomial and spherical fits. The continuous TLS method enables the creation of mathematically traceable reference pairs suitable for the assessment of form removal algorithms in surface texture analysis software. Multiple example reference pairs are presented and used to assess the performance of four tested surface texture analysis software packages. The results of each software are compared against the mathematical reference, highlighting their strengths and weaknesses.

Abstract This paper reports the results of an investigation whose objective is to find which slope conceptualizations have a presence in high school mathematics textbooks and which are the predominant ones. For this, we used the Content Analysis method, where the objects of analysis are found in content exposition, worked examples, and in the exercises or problems proposed in the textbooks. As a reference framework we used the eleven slope conceptualizations identified by Stump (1999) and Moore-Russo, Conner and Rugg (2011). Our findings indicate the presence of most of the conceptualizations identified in the previous research, however, there is a notable predominance of those that emerge from the analytical definition of slope, such as the parametric coefficient, algebraic ratio, and trigonometric conception and its internal application in determination of parallelism or perpendicularity between lines as is the determining property. These conceptualizations, on the one hand, induce to formation of the idea that slope makes sense only in intra-mathematical context, and on the other hand, they favor the development of procedural knowledge on detriment of conceptual knowledge. Understanding the slope requires the creation of internal networks as a product of connections between conceptualizations intra and extra mathematical plane, in addition to the harmonious development of conceptual and procedural knowledge. Achieving the understanding of the concepts is essential for Mathematics Education, however, our results indicate that the texts used by teachers can hardly contribute to this achievement.

CONTEXT

Practice Scenario: The UIW School of Engineering wants to recruit more students into their program. They will recruit students with great math scores. Also, to increase the chances of recruitment,​ the department will look for students who qualify for financial aid. Students who qualify for financial aid more than likely come from low socio-economic backgrounds. One way to indicate this is to view how much federal revenue a school district receives through its state. High federal revenue for a school indicates that a large portion of the student base comes from low incomes families.

The question we wish to ask is as follows: Name the school districts across the nation where their Child Nutrition Programs(c25) are federally funded between the amounts $30,000 and $50,000. And where the average math score for the school districts corresponding state is greater than or equal to the nations average score of 282.

The SQL query below in 'Top5MathTarget.sql' can be used to answer this question in MySQL. To execute this process, one would need to install MySQL to their local system and load the attached datasets below from Kaggle into their MySQL schema. The SQL query below will then join the separate tables on various key identifiers.

DATA SOURCE Data is sourced from The U.S Census Bureau and The Nations Report Card (using the NAEP Data Explorer).

Finance: https://www.census.gov/programs-surveys/school-finances/data/tables.html

Math Scores: https://www.nationsreportcard.gov/ndecore/xplore/NDE

COLUMN NOTES

All data comes from the school year 2017. Individual schools are not represented, only school districts within each state.

FEDERAL FINANCE DATA DEFINITIONS

t_fed_rev: Total federal revenue through the state to each school district.

C14- Federal revenue through the state- Title 1 (no child left behind act).

C25- Federal revenue through the state- Child Nutrition Act.

Title 1 is a program implemented in schools to help raise academic achievement ​for all students. The program is available to schools where at least 40% of the students come from low inccom​​e families.

Child Nutrition Programs ensure the children are getting the food they need to grow and learn. Schools with high federal revenue to these programs indicate students that also come from low income​ families.

MATH SCORES DATA DEFINITIONS

Note: Mathematics, Grade 8, 2017, All Students (Total)

average_scale_score - The state's average score for eighth graders taking the NAEP math exam.

% of pupils achieving 5+ A*-Cs GCSE inc. English & Maths at Key Stage 4 (new First Entry definition) - (Snapshot) *This indicator has been discontinued due to national changes in GCSEs in 2016.

READ ME

Welcome to the Universal Binary Principle (UBP) Dictionary System - Version 2

Author: Euan Craig, New Zealand 2025

Embark on a revolutionary journey with Version 2 of the UBP Dictionary System, a cutting-edge Python notebook that redefines how words are stored, analyzed, and visualized! Built for Kaggle, this system encodes words as multidimensional hexagonal structures in custom .hexubp files, leveraging sophisticated mathematics to integrate binary toggles, resonance frequencies, spatial coordinates, and more, all rooted in the Universal Binary Principle (UBP). This is not just a dictionary—it’s a paradigm shift in linguistic representation.

What is the UBP Dictionary System? The UBP Dictionary System transforms words into rich, vectorized representations stored in custom .hexubp files—a JSON-based format designed to encapsulate a word’s multidimensional UBP properties. Each .hexubp file represents a word as a hexagonal structure with 12 vertices, encoding: * Binary Toggles: 6-bit patterns capturing word characteristics. * Resonance Frequencies: Derived from the Schumann resonance (7.83 Hz) and UBP Pi (~2.427). * Spatial Vectors: 6D coordinates positioning words in a conceptual “Bitfield.” * Cultural and Harmonic Data: Contextual weights, waveforms, and harmonic properties.

These .hexubp files are generated, managed, and visualized through an interactive Tkinter-based interface, making the system a powerful tool for exploring language through a mathematical lens.

Unique Mathematical Foundation The UBP Dictionary System is distinguished by its deep reliance on mathematics to model language: * UBP Pi (~2.427): A custom constant derived from hexagonal geometry and resonance alignment (calculated as 6/2 * cos(2π * 7.83 * 0.318309886)), serving as the system’s foundational reference. * Resonance Frequencies: Frequencies are computed using word-specific hashes modulated by UBP Pi, with validation against the Schumann resonance (7.83 Hz ± 0.078 Hz), grounding the system in physical phenomena. * 6D Spatial Vectors: Words are positioned in a 6D Bitfield (x, y, z, time, phase, quantum state) based on toggle sums and frequency offsets, enabling spatial analysis of linguistic relationships. * GLR Validation: A non-corrective validation mechanism flags outliers in binary, frequency, and spatial data, ensuring mathematical integrity without compromising creativity.

This mathematical rigor sets the system apart from traditional dictionaries, offering a framework where words are not just strings but dynamic entities with quantifiable properties. It’s a fusion of linguistics, physics, and computational theory, inviting users to rethink language as a multidimensional phenomenon.

Comparison with Other Data Storage Mechanisms The .hexubp format is uniquely tailored for UBP’s multidimensional model. Here’s how it compares to other storage mechanisms, with metrics to highlight its strengths: CSV/JSON (Traditional Dictionaries): * Structure: Flat key-value pairs (e.g., word:definition). * Storage: ~100 bytes per word for simple text (e.g., “and”:“conjunction”). * Query Speed: O(1) for lookups, but no support for vector operations. * Limitations: Lacks multidimensional data (e.g., spatial vectors, frequencies). * .hexubp Advantage: Stores 12 vertices with vectors (~1-2 KB per word), enabling complex analyses like spatial clustering or frequency drift detection.

Relational Databases (SQL): * Structure: Tabular, with columns for word, definition, etc. * Storage: ~200-500 bytes per word, plus index overhead. * Query Speed: O(log n) for indexed queries, slower for vector computations. * Limitations: Rigid schema, inefficient for 6D vectors or dynamic vertices. * .hexubp Advantage: Lightweight, file-based (~1-2 KB per word), with JSON flexibility for UBP’s hexagonal model, no database server required.

Vector Databases (e.g., Word2Vec): * Structure: Fixed-dimension vectors (e.g., 300D for semantic embeddings). * Storage: ~2.4 KB per word (300 floats at 8 bytes each). * Query Speed: O(n) for similarity searches, optimized with indexing. * Limitations: Generic embeddings lack UBP-specific dimensions (e.g., resonance, toggles). * .hexubp Advantage: Smaller footprint (~1-2 KB), with domain-specific dimensions tailored to UBP’s theoretical framework.

Graph Databases: * Structure: Nodes and edges for word relationships. * Storage: ~500 bytes per word, plus edge overhead. * Query Speed: O(k) for traversals, where k is edge count. * Limitations: Overkill for dictionary tasks, complex setup. * .hexubp Advantage: Self-contained hexagonal structure per word, simpler for UBP’s needs, with comparable storage (~1-2 KB).

The .hexubp format balances storage efficiency, flexibility, and UBP-s...

Protein-Protein, Genetic, and Chemical Interactions for MATH-39 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: MATH (meprin-associated Traf homology) domain containing

Protein-Protein, Genetic, and Chemical Interactions for MATH-34 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: Protein MATH-34

Protein-Protein, Genetic, and Chemical Interactions for MATH-41 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: MATH (meprin-associated Traf homology) domain containing

The HWRT database of handwritten symbols contains on-line data of handwritten symbols such as all alphanumeric characters, arrows, greek characters and mathematical symbols like the integral symbol.

The database can be downloaded in form of bzip2-compressed tar files. Each tar file contains:

• symbols.csv: A CSV file with the rows symbol_id, latex, training_samples, test_samples. The symbol id is an integer, the row latex contains the latex code of the symbol, the rows training_samples and test_samples contain integers with the number of labeled data.
• train-data.csv: A CSV file with the rows symbol_id, user_id, user_agent and data.
• test-data.csv: A CSV file with the rows symbol_id, user_id, user_agent and data.

All CSV files use ";" as delimiter and "'" as quotechar. The data is given in YAML format as a list of lists of dictinaries. Each dictionary has the keys "x", "y" and "time". (x,y) are coordinates and time is the UNIX time.

About 90% of the data was made available by Daniel Kirsch via github.com/kirel/detexify-data. Thank you very much, Daniel!

Context

Publicly available datasets have helped the computer vision community to compare new algorithms and develop applications. Especially MNIST [LBBH98] was used thousands of times to train and evaluate models for classification. However, even rather simple models consistently get about 99.2 % accuracy on MNIST [TF-16a]. The best models classify everything except for about 20 instances correct. This makes meaningful statements about improvements in classifiers hard. A possible reason why current models are so good on MNIST are 1) MNIST has only 10 classes 2) there are very few (probably none) labelling errors in MNIST 3) every class has 6000 training samples 4) the feature dimensionality is comparatively low. Also, applications that need to recognize only Arabic numerals are rare. Similar to MNIST, HASY is of very low resolution. In contrast to MNIST, the HASYv2 dataset contains 369 classes, including Arabic numerals and Latin characters. Furthermore, HASYv2 has much fewer recordings per class than MNIST and is only in black and white whereas MNIST is in grayscale. HASY could be used to train models for semantic segmentation of non-cursive handwritten documents like mathematical notes or forms.

Content

The dataset contains the following:

• a pickle file: HASYv2
• a txt file: cite.txt

The pickle file contains the 168233 observations in a dictionary form. The simplest way to use the HASYv2 dataset is to download the pickle file below (HASYv2). You can use the following lines of code to load the data:

def unpickle(file):
  import pickle
  with open(file, 'rb') as fo:
    dict = pickle.load(fo, encoding='bytes')
  return dict

HASYv2 = unpickle("HASYv2")

The data comes in a dictionary format, you can get the data and the labels separately by extracting the content from the dictionary: data = HASYv2['data'] labels = HASYv2['labels'] symbols = HASYv2['latex_symbol'] Note that the shape of the data is directly (32 x 32 x 3 x 168233), with the first and second dimensions as the height and width respectively, the third dimension correspond to the channels and the fourth to the observation number.

Citation

fedesoriano. (October 2021). HASYv2 - Symbol Recognizer. Retrieved [Date Retrieved] from https://www.kaggle.com/fedesoriano/hasyv2-symbol-recognizer.

Source

The dataset was originally uploaded by Martin Thoma, see https://arxiv.org/abs/1701.08380.

Thoma, M. (2017). The HASYv2 dataset. ArXiv, abs/1701.08380.

The original paper describes the HASYv2 dataset. HASY is a publicly available, free of charge dataset of single symbols similar to MNIST. It contains 168233 instances of 369 classes. HASY contains two challenges: A classification challenge with 10 pre-defined folds for 10-fold cross-validation and a verification challenge. The HASYv2 dataset (PDF Download Available). Available from: https://arxiv.org/pdf/1701.08380.pdf [accessed Oct 11, 2021].

Protein-Protein, Genetic, and Chemical Interactions for MATH-42 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: Protein MATH-42

Protein-Protein, Genetic, and Chemical Interactions for MATH-14 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: Protein MATH-14

Abstract The CADNA library enables one to estimate, using a probabilistic approach, round-off error propagation in any simulation program. CADNA provides new numerical types, the so-called stochastic types, on which round-off errors can be estimated. Furthermore CADNA contains the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. On 64-bit processors, depending on the...

Title of program: CADNA Catalogue Id: AEAT_v1_1

Nature of problem A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time.

Versions of this program held in the CPC repository in Mendeley Data AEAT_v1_0; CADNA; 10.1016/j.cpc.2008.02.003 AEAT_v1_1; CADNA; 10.1016/j.cpc.2010.07.012

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)