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.

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-48 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: MATH (meprin-associated Traf homology) domain containing

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...

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.

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.

This dataset contains metadata (title, abstract, date of publication, field, etc) for around 1 million academic articles. Each record contains additional information on the country of study and whether the article makes use of data. Machine learning tools were used to classify the country of study and data use.

Our data source of academic articles is the Semantic Scholar Open Research Corpus (S2ORC) (Lo et al. 2020). The corpus contains more than 130 million English language academic papers across multiple disciplines. The papers included in the Semantic Scholar corpus are gathered directly from publishers, from open archives such as arXiv or PubMed, and crawled from the internet.

We placed some restrictions on the articles to make them usable and relevant for our purposes. First, only articles with an abstract and parsed PDF or latex file are included in the analysis. The full text of the abstract is necessary to classify the country of study and whether the article uses data. The parsed PDF and latex file are important for extracting important information like the date of publication and field of study. This restriction eliminated a large number of articles in the original corpus. Around 30 million articles remain after keeping only articles with a parsable (i.e., suitable for digital processing) PDF, and around 26% of those 30 million are eliminated when removing articles without an abstract. Second, only articles from the year 2000 to 2020 were considered. This restriction eliminated an additional 9% of the remaining articles. Finally, articles from the following fields of study were excluded, as we aim to focus on fields that are likely to use data produced by countries’ national statistical system: Biology, Chemistry, Engineering, Physics, Materials Science, Environmental Science, Geology, History, Philosophy, Math, Computer Science, and Art. Fields that are included are: Economics, Political Science, Business, Sociology, Medicine, and Psychology. This third restriction eliminated around 34% of the remaining articles. From an initial corpus of 136 million articles, this resulted in a final corpus of around 10 million articles.

Due to the intensive computer resources required, a set of 1,037,748 articles were randomly selected from the 10 million articles in our restricted corpus as a convenience sample.

The empirical approach employed in this project utilizes text mining with Natural Language Processing (NLP). The goal of NLP is to extract structured information from raw, unstructured text. In this project, NLP is used to extract the country of study and whether the paper makes use of data. We will discuss each of these in turn.

To determine the country or countries of study in each academic article, two approaches are employed based on information found in the title, abstract, or topic fields. The first approach uses regular expression searches based on the presence of ISO3166 country names. A defined set of country names is compiled, and the presence of these names is checked in the relevant fields. This approach is transparent, widely used in social science research, and easily extended to other languages. However, there is a potential for exclusion errors if a country’s name is spelled non-standardly.

The second approach is based on Named Entity Recognition (NER), which uses machine learning to identify objects from text, utilizing the spaCy Python library. The Named Entity Recognition algorithm splits text into named entities, and NER is used in this project to identify countries of study in the academic articles. SpaCy supports multiple languages and has been trained on multiple spellings of countries, overcoming some of the limitations of the regular expression approach. If a country is identified by either the regular expression search or NER, it is linked to the article. Note that one article can be linked to more than one country.

The second task is to classify whether the paper uses data. A supervised machine learning approach is employed, where 3500 publications were first randomly selected and manually labeled by human raters using the Mechanical Turk service (Paszke et al. 2019).[1] To make sure the human raters had a similar and appropriate definition of data in mind, they were given the following instructions before seeing their first paper:

Each of these documents is an academic article. The goal of this study is to measure whether a specific academic article is using data and from which country the data came.

There are two classification tasks in this exercise:

1. identifying whether an academic article is using data from any country

2. Identifying from which country that data came.

For task 1, we are looking specifically at the use of data. Data is any information that has been collected, observed, generated or created to produce research findings. As an example, a study that reports findings or analysis using a survey data, uses data. Some clues to indicate that a study does use data includes whether a survey or census is described, a statistical model estimated, or a table or means or summary statistics is reported.

After an article is classified as using data, please note the type of data used. The options are population or business census, survey data, administrative data, geospatial data, private sector data, and other data. If no data is used, then mark "Not applicable". In cases where multiple data types are used, please click multiple options.[2]

For task 2, we are looking at the country or countries that are studied in the article. In some cases, no country may be applicable. For instance, if the research is theoretical and has no specific country application. In some cases, the research article may involve multiple countries. In these cases, select all countries that are discussed in the paper.

We expect between 10 and 35 percent of all articles to use data.

The median amount of time that a worker spent on an article, measured as the time between when the article was accepted to be classified by the worker and when the classification was submitted was 25.4 minutes. If human raters were exclusively used rather than machine learning tools, then the corpus of 1,037,748 articles examined in this study would take around 50 years of human work time to review at a cost of $3,113,244, which assumes a cost of $3 per article as was paid to MTurk workers.

A model is next trained on the 3,500 labelled articles. We use a distilled version of the BERT (bidirectional Encoder Representations for transformers) model to encode raw text into a numeric format suitable for predictions (Devlin et al. (2018)). BERT is pre-trained on a large corpus comprising the Toronto Book Corpus and Wikipedia. The distilled version (DistilBERT) is a compressed model that is 60% the size of BERT and retains 97% of the language understanding capabilities and is 60% faster (Sanh, Debut, Chaumond, Wolf 2019). We use PyTorch to produce a model to classify articles based on the labeled data. Of the 3,500 articles that were hand coded by the MTurk workers, 900 are fed to the machine learning model. 900 articles were selected because of computational limitations in training the NLP model. A classification of “uses data” was assigned if the model predicted an article used data with at least 90% confidence.

The performance of the models classifying articles to countries and as using data or not can be compared to the classification by the human raters. We consider the human raters as giving us the ground truth. This may underestimate the model performance if the workers at times got the allocation wrong in a way that would not apply to the model. For instance, a human rater could mistake the Republic of Korea for the Democratic People’s Republic of Korea. If both humans and the model perform the same kind of errors, then the performance reported here will be overestimated.

The model was able to predict whether an article made use of data with 87% accuracy evaluated on the set of articles held out of the model training. The correlation between the number of articles written about each country using data estimated under the two approaches is given in the figure below. The number of articles represents an aggregate total of

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

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-34 (Caenorhabditis elegans) curated by BioGRID (https://thebiogrid.org); DEFINITION: Protein MATH-34

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

The release of the LCA Commons Unit Process Data: field crop production Version 1.1 includes the following updates:Added meta data to reflect USDA LCA Digital Commons data submission guidance including descriptions of the process (reference to which the size of the inputs and outputs in the process relate, description of the process and technical scope and any aggregation; definition of the technology being used, its operating conditions); temporal representatives; geographic representativeness; allocation methods; process type (U: unit process, S: system process); treatment of missing intermediate flow data; treatment of missing flow data to or from the environment; intermediate flow data sources; mass balance; data treatment (description of the methods and assumptions used to transform primary and secondary data into flow quantities through recalculating, reformatting, aggregation, or proxy data and a description of data quality according to LCADC convention); sampling procedures; and review details. Also, dataset documentation and related archival publications are cited in the APA format.Changed intermediate flow categories and subcategories to reflect the ISIC International Standard Industrial Classification (ISIC).Added “US-” to the US state abbreviations for intermediate flow locations.Corrected the ISIC code for “CUTOFF domestic barge transport; average fuel” (changed to ISIC 5022: Inland freight water transport).Corrected flow names as follows: "Propachlor" renamed "Atrazine". “Bromoxynil octanoate” renamed “Bromoxynil heptanoate”. “water; plant uptake; biogenic” renamed “water; from plant uptake; biogenic” half the instances of “Benzene, pentachloronitro-“ replaced with Etridiazole and half with “Quintozene”. “CUTOFF phosphatic fertilizer, superphos. grades 22% & under; at point-of-sale” replaced with “CUTOFF phosphatic fertilizer, superphos. grades 22% and under; at point-of-sale”.Corrected flow values for “water; from plant uptake; biogenic” and “dry matter except CNPK; from plant uptake; biogenic” in some datasets.Presented data in the International Reference Life Cycle Data System (ILCD)1 format, allowing the parameterization of raw data and mathematical relations to be presented within the datasets and the inclusion of parameter uncertainty data. Note that ILCD formatted data can be converted to the ecospold v1 format using the OpenLCA software.Data quality rankings have been updated to reflect the inclusion of uncertainty data in the ILCD formatted data.Changed all parameter names to “pxxxx” to accommodate mathematical relation character limitations in OpenLCA. Also adjusted select mathematical relations to recognize zero entries. The revised list of parameter names is provided in the documentation attached.Resources in this dataset:Resource Title: Cooper-crop-production-data-parameterization-version-1.1 .File Name: Cooper-crop-production-data-parameterization-version-1.1.xlsxResource Description: Description of parameters that define the Cooper Unit process data for field crop production version 1.1Resource Title: Cooper_Crop_Data_v1.1_ILCD.File Name: Cooper_Crop_Data_v1.1_ILCD.zipResource Description: .zip archive of ILCD xml files that comprise crop production unit process modelsResource Software Recommended: openLCA,url: http://www.openlca.org/Resource Title: Summary of Revisions of the LCA Digital Commons Unit Process Data: field crop production for version 1.1 (August 2013).File Name: Summary of Revisions of the LCA Digital Commons Unit Process Data- field crop production, Version 1.1 (August 2013).pdfResource Description: Documentation of revisions to version 1 data that constitute version 1.1

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

Supplementary Materials for Chapter 3 of the Doctoral Dissertation "How we think about numbers - Early counting and mathematical abstraction". Contains open data and materials.As children learn to count, they make one of their first mathematical abstractions. They initially learn how numbers in the count sequence correspond to quantities of physical things if the rules of counting are followed (i.e., if you say the numbers in order “one two three four …” as you tag each thing with a number). Around the age of four-years-old, children discover that these rules also define numbers in relation to each other, such that numbers contain meaning in themselves and without reference to the physical world (e.g., “five” is “one” more than “four”). It is through learning to count, that children discover the natural numbers as mathematical symbols defined by abstract rules.In this dissertation, I explored the developmental trajectory and the cognitive mechanisms of how we gain an understanding of the natural numbers as children. I present new methodological, empirical, and theoretical insights on how and when in the process of learning to count, children discover that numbers represent cardinalities, that numbers can be defined in relation to each other by the successor function and that numbers refer to units. Lastly, I explore this mathematical abstraction as the foundation of how we think about numbers as adults.My work critically tested prominent theories on how learning to count gives meaning to numbers through analogical mapping and conceptual bootstrapping. Findings across five empirical studies suggest that the process is more gradual and continuous than previous theories have proposed. Children begin to understand numbers as cardinalities defined in relation to other numbers by the successor function before they fully grasp the rules of counting. With learning the rules of counting this understanding continuously expands and matures. I further suggest that children may only fully understand numbers as abstract mathematical symbols once they understand how counting and numbers refer to the abstract notion of units rather than to physical things.The central finding of this dissertation is that learning to count does not change children’s understanding of numbers altogether and all at once. Nonetheless, when learning to count, children accomplish a fascinating mathematical abstraction, which builds the foundation for lifelong mathematical learning.© Theresa Elise Wege, CC BY-NC 4.0

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)

Gerhard Ris former lawyer and magistrate with thirty years of experience in courts of law

Inverse final statements

· Science Starts with Descartes & Discarding Descartes

· The proper scientific procedure for starting with inverse final statements is as long as needed and as short as possible.

· Flying an aircraft in an emergency is also scientific in science proper.

· Producing proper science requires a multi-majority consensus in eight departments of the collective instrument brain, which can be achieved by following its now-available Train Your Intuitive Brain instruction manual the One Law of Human Nature.

· Teaching Empowerment White Magic Illusionism alas also teaches Black Magic illusionism

· Being Empowered by White or Black Magic Illusionism has immediate rewards

· Deciding to do the proposed Oracle Senate Test by any oligarch such as the Dutch Research Council NWO will instantly shift the paradigm, producing peace and prosperity for all and especially benefiting NATO.

· Homo Sapiens hasn’t even lived for one galactic year and is nearing extinction playing with nukes.

· The One Law of Human Nature proves that most mathematicians and physicists are, as a genotype, deep idiots at more than average complex geometry. Yet they have oligarch power in science via improper peer review. They use computers to fraudulently claim to be the best at complex geometry because they are indeed best at computing.

· The current paradigm procedure requires naming, shaming, and ridiculing NWO for failing the improved Elementary Scientist Exam as science proper.

· This can best be done by other than Dutch scientists who aren’t dependent on funding from NWO because the effect is global.

· NWO thus isn’t certified as a reliable source for funding Elementary Science and Education like Dada Easter Bunny.

· Current science incorrectly doesn’t accept humour and relativism as a per definition essential part of the marketing, advertisement, and sales of science. Current science demands autistic deadly serious tediously dull conscientiousness a deadly sin in artistic R&D.

· Current science and NWO don’t have a definition of science or pseudo-science other than oligarchs of science peer review deem to be scientific. This falsifies current science on elementary issues.

· NWO is most guilty of the mainstream woke madness in most universities which is antifeminism, racist slaveholding egotrip of gender-neutral female logic better seen as sales management/ HRM hypnotic relation manipulation. A Bayesian inversion of the synapse in the instrument brain. Needing to keep antifeminism, racism, and slavery going because otherwise losing their meaning in life.

· NWO is also most guilty of the anti-scientific polarisation against science and scientists in society as a reaction to the actions of wokeism.

· NWO primarily caused the serious intended cuts in science and education in the Netherlands.

· NWO is a representative of the greatest bosses of god delusion of the god that doesn’t listen.

· NWO represents a criminally insane personality cult that for 5000 years has successfully built ever better “unsinkable” Titanics and sunk them in the same peat-burn-like genocidal iceberg scenario.

· When you do the same the same happens.

· The Oracle Senate Test is akin to the first flight of a prototype exclusively built out of successfully tested parts.

· The New Secretary General of NATO nearly decided to do the then still too taboo even for PM Mr. Teflon's radical plan for new governance Oracle Senate Test by an emergency law in the Omtzigt affaire.

· More than 99.9% of Old School tried and tested Sun Tzu's Art of War to never corner one's opponent and always build them a Golden Bridge way out.

· Save Our Mighty Billionaires and all other oligarchs like NWO!

· The cosmos/ everything is proven on the beginning of absolute proof in the reductio ad absurdum that our instrument brain thinks in an everything not only nothing and observes One Law of Nature that is absolute without contradictions including loopholes by far proven best practice circumstantial evidence proof with only data pro and absolutely no data con in all of several fields DOI published in proper peer review with access to all the raw data. Completely theorem based on what all the science was in, ages ago only requiring a few new easy twists to solve. The validation rises every time no valid opposition is met on the inherently circular argument claim that workability (werkelijkheid in Dutch) is an infinite topology of truths and infinite realities that only seemingly ever contradict in one of infinite parallel and in-line Nirvana movie scenario compositions achieving very practical workability (werkbaarheid in Dutch)

· Everything of the deterministic meaningless cosmos has infinite separate elements of classical mechanical Eucledian 3D geometry mass atomos movable connections that interact akin to snowballs in one 3D Euclidian empty space ether. The observed absence of evidence only leaves room for illegal unreasonable doubt on the correct definition of science which is further improved in this article. The 3rd law of everything as an undividable part of the ten dualistic laws of one law of nature dictates the scientific goal by one law of human nature the decent survival of homo sapiens that life has meaning and free will. The cosmos is both quantified and continuous at the same time in infinite time. Time is a thought and a thought is interactive moving timeless mass. Mass is internally absolutely motionless and thus can not be described by the notion of time. Mass is lifeless. Mass produces matter in a proto-DNA waving life non-waving proto-death cycle. Internal waves are proto-DNA consciousness memory bank of intelligent action is intelligent reaction infinite past moving toward an infinite future.

· Homo sapiens are proven to be robots that must inherently religiously believe not to be robots to hedge the bets on the goal of decent survival. The easiest to detect is the 1/64 specific sort of genotype of anyone which is also the greatest predictor of human behavior. In decreasing predictive order on behavior, the model proves phenotype (deeply religious), religious type, hypnotic (slightly religious)type, and unique type that all must be taken into account. This can only be done by the well-trained brain in an intuitive brain as part of a team with Bildung.

· The model proves that bashing opens a new market in litigation. This should be done via advertisement and sales techniques. This can only be achieved by any oligarch like NWO. NWO is in the know and is thus the easiest prey. Observe the thumbnails as the posters that science proper demands at the end of this article. These are a startup of the classes that as remedial teaching should be given in universities because they weren’t given in high school.

RECAP EXCERPT DOI PUBLICATIONS

Add this trial and erratum to my last publication