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.

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, which presents a substantial risk of model overfitting and fails to accurately represent genuine mathematical… See the full description on the dataset page: https://huggingface.co/datasets/PremiLab-Math/MathCheck.

Abstract Within the line of teacher training, we present in this work aspects of a research with future elementary school teachers, where we focus on understanding how students of the University of Granada interpret the objective as an analysis element of a school mathematical task, framed within the Didactic Analysis as a functional tool in the initial formation. A qualitative methodology has been followed through content analysis. The antecedents show the importance of the school tasks to favor mathematics learning and the results show us the difficulty that the future teachers present to establish and to define the objective of a school mathematical task.

These datatasets relate to the computational study presented in the paper The Berth Allocation Problem with Channel Restrictions, authored by Paul Corry and Christian Bierwirth. They consist of all the randomly generated problem instances along with the computational results presented in the paper.

Results across all problem instances assume ship separation parameters of [delta_1, delta_2, delta_3] = [0.25, 0, 0.5].

Excel Workbook Organisation:

The data is organised into separate Excel files for each table in the paper, as indicated by the file description. Within each file, each row of data presented (aggregating 10 replications) in the corrsponding table is captured in two worksheets, one with the problem instance data, and the other with generated solution data obtained from several solution methods (described in the paper). For example, row 3 of Tab. 2, will have data for 10 problem instances on worksheet T2R3, and corresponding solution data on T2R3X.

Problem Instance Data Format:

On each problem instance worksheet (e.g. T2R3), each row of data corresponds to a different problem instance, and there are 10 replications on each worksheet.

The first column provides a replication identifier which is referenced on the corresponding solution worksheet (e.g. T2R3X).

Following this, there are n*(2c+1) columns (n = number of ships, c = number of channel segmenets) with headers p(i)_(j).(k)., where i references the operation (channel transit/berth visit) id, j references the ship id, and k references the index of the operation within the ship. All indexing starts at 0. These columns define the transit or dwell times on each segment. A value of -1 indicates a segment on which a berth allocation must be applied, and hence the dwell time is unkown.

There are then a further n columns with headers r(j), defining the release times of each ship.

For ChSP problems, there are a final n colums with headers b(j), defining the berth to be visited by each ship. ChSP problems with fixed berth sequencing enforced have an additional n columns with headers toa(j), indicating the order in which ship j sits within its berth sequence. For BAP-CR problems, these columnns are not present, but replaced by n*m columns (m = number of berths) with headers p(j).(b) defining the berth processing time of ship j if allocated to berth b.

Solution Data Format:

Each row of data corresponds to a different solution.

Column A references the replication identifier (from the corresponding instance worksheet) that the soluion refers to.

Column B defines the algorithm that was used to generate the solution.

Column C shows the objective function value (total waiting and excess handling time) obtained.

Column D shows the CPU time consumed in generating the solution, rounded to the nearest second.

Column E shows the optimality gap as a proportion. A value of -1 or an empty value indicates that optimality gap is unknown.

From column F onwards, there are are n*(2c+1) columns with the previously described p(i)_(j).(k). headers. The values in these columns define the entry times at each segment.

For BAP-CR problems only, following this there are a further 2n columns. For each ship j, there will be columns titled b(j) and p.b(j) defining the berth that was allocated to ship j, and the processing time on that berth respectively.

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.

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...

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.

International Mathematical Olympiad (IMO) Data

This data comes from International Mathematical Olympiad (IMO).

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents. The competition consists of 6 problems and is held over two consecutive days with 3 problems each.

1. How have country rankings shifted over time?
2. What is the distribution of participation by gender? What's the distribution of top scores?
3. How does team size or team composition (e.g., number of first-time participants vs. veterans) relate to overall country performance?

Data Dictionary

country_results_df.csv

individual_results_df.csv

timeline_df.csv

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...

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

G_crack_length.csv

Dataset Summary GSM8K (Grade School Math 8K) is a dataset of 8.5K high quality linguistically diverse grade school math word problems. The dataset was created to support the task of question answering on basic mathematical problems that require multi-step reasoning.

These problems take between 2 and 8 steps to solve. Solutions primarily involve performing a sequence of elementary calculations using basic arithmetic operations (+ − ×÷) to reach the final answer. A bright middle school student should be able to solve every problem: from the paper, "Problems require no concepts beyond the level of early Algebra, and the vast majority of problems can be solved without explicitly defining a variable." Solutions are provided in natural language, as opposed to pure math expressions. From the paper: "We believe this is the most generally useful data format, and we expect it to shed light on the properties of large language models’ internal monologues"

This dataset was converted from https://github.com/openai/prm800k using the following script. import json import os from datasets import Dataset, DatasetDict

def generate_data(data_path: str): with open(data_path, "r", encoding="utf-8") as f: for line in f: data = json.loads(line) yield { "problem": data["problem"], "answer": data["answer"], }

def main(): trainset = Dataset.from_generator(generate_data… See the full description on the dataset page: https://huggingface.co/datasets/hiyouga/math12k.

The First Law of Everything (LOE)/ Law of Nature (Newton)

1st LOE CLASSICAL MECHANICS viewed by homo sapiens for homo sapiens in the derived 1st local law the Law of Human Nature 1st LHN Completeness. Before judging, always try to get the whole Nirvana movie scenario/ composition picture viewed in a thus holistic dualistic reductio ad absurdum way by mentally splitting the unsplittable of the incomplete subset Nirvana movie, you are in, of the superset Nirvana movie. 1st LOE the only one remaining axiomatic assumption is one Consistent hence completely noncontradictory loophole-free everything/cosmos. This defines the falsifying ‘absurd’ qualification. The largest combining super set that can and must as exclusive parts of the whole be described using a few slight twists by the five laws of thermodynamics: 0th LTD Mass Inertia Kg remains perpetually identical on a cosmological timescale in super set and smallest set (Lifeless, timeless, meaningless, non free will robotics); 1st LTD Conservation of Energy relative moving action is reaction mass on a cosmological timescale (Intelligent action is intelligent reaction); 2nd LTD mounting & declining complexity mass connections disconnections with permenent and non permenent uniquely movable identicle sorts of connections of identical mass Entropy Cycle on a cosmological timescale (Unique temporary local Consious memory banks); 3d LTD in Perpetual Action Reaction identical repetative within limits unique motion on a cosmological timescale (Identical History repeats itself in a unique way); 4th LTD every object has an Incidental Maximum Velocity the smallest element of nigh 10c during the smallest timescale under incidental maximum resounding non wave pressure on a cosmological timescale. (Life-death cycle with meaning and free will, is a deep religious dictate requiring seemingly contradictory deterministic statistics)

2nd LOE DETERMINISTIC STATISTICS (Gauss)/ 2nd LHN Normality Humans should act freely within the deterministic boundaries of ‘The Law’. 2nd LOE The five dualistic quantified toothed wheel-like and continuous smooth wheel-like normal/ ‘conform the norm’ distributions from which all other distributions can/ must be derived: 1. Combining Bell curve distribution; 2. Flat distribution; 3. Edge distribution; 4. Broken distribution; 5. Curved distribution. (Double helix DNA, Learning curve, Fair Dirty Distributions requiring a procedure for proof)

3rd LOE PROOF PROCEDURE Laplace’s theorem formula works consistently defined both deterministically and probabilistically: Pure mathematical non-physics data thus ‘unreasonable doubt’ requires many axiomatic assumptions based logic formula & Bayesian applied/ dirty ‘beyond reasonable doubt’ mathematics of the physics of nature dicates that consistent input means consistent output and inconsistent input means inconsistent output by the Laplace formula given only one Bayesian axiomatic assumption based on a beginning of absolute proof on a consistently defined valued goal. Given the norm of risk as chance times valued consequence acceptable input providing ratios of chance pro versus chance con as probabilities. Prior Odds multiplied by the Independent Likelihood Ratios, provide the Posterior Odds as the new Prior Odds of the endless trial and error evidence-based cycle. 3rd LHN Procedure It’s Intuitive Common Sense to take your own robotically induced feelings as facts in the five salads that are fit for human consumption: 1. The combining One Mixed Salad, 2. Word Salads 3. Picture Salads 4. Course Number Salads 5. Fine Number Salads of this Socratic Yin & Yang Harry Potter formula as the recipe/ algorithm for the proper proof procedure that is consistent with the synapse of the instrument brain of all mammals, which is consistent with the everything cosmos as the symbiotics of which require the waves of this collective to come to more order than the current laws of nature can explain.

4. LOE ORDER (Euclidian Geometry)

The greatest breakthrough was due to my early age Bildung on Evidence-Based-Medicine as originally intended: rational use of gut feelings 1960-1980, my Just Proof legal model 1990, my Incomplete Higgs-graviton physics model LOE 2010, my Block-model Brain 2014, LOE 2017 & Integrating All Mathematical Mixed Salads Euclidean Geometry 1-Neutrino 2023 into ‘The Law’. And subsequent constant tweaking of the presentation. First published under peer review following The Law in NWA 2015 search terms “casus ZPE” “het vergeten instrument tussen de oren”.

Behold the most succinct presentation of the Train Your Brain instruction manual for using the collective and individual instrument brains as the 4th LOE on one A4. The elaborated model is DOI published in the Elementary List. The 4th LOE is the soul as the order function of the cosmos and our brain. The images are in the download version.

5th LOE ZERO IS ONE LENGTH (Euler’s identity) -1 + 1 =0 or e^(iPi) + 1 =0 zero has a length which is not empty as part of the ruler's massive measuring device. This is consistent with and constitutes the fact (taken as 100% true) that every non-empty sign element of mass must exist in workability. And that irrational numbers become rational in infinity, not needing imaginary numbers anymore, not being lengths ‘i’, or measurement lengths for corner ‘e’ or circle lengths ‘Pi’. This is proven as a reductio ad absurdum, the strongest proof based on the beginning of absolute proof in the 3rd LOE. i.e. based on the fingerprint of the absolutely proven culprit, Mother Nature is on the mass murder weapon mass and not on matter as elementary. On a lower probative value, because more complex means it is less reliable, the proven way how the main suspect for further investigation is the Lego-Velcro particle built out of 500 identical massive rings in 10% double connections, 40% triple connections, 40% quadruple connections and 10% cinque connections creating the four inertias of the fifth unique chainmail combining enertia algorithms creating the snowflake function for the ice-wall pressure vessel/ snowball larger particle everything cosmos solely built out of snowflakes in empty space. This is an intuitive associative testable artistically creative guess. You either can or can’t build such a particle out of these elements via further quick and dirty reverse engineering. All known constants need to be reverse-engineered into this one particle. It might then show that every particle must have 501 rings instead of 500. ‘The Law’ dictates that the burden of proof via investigation lies with current science. The antithesis that it’s proven unsolvable via John Bell's inequality theorem is consistent with ‘The Law’ because of a proven string of fallacies in reasoning that are only consistent to be the greatest bosses of god in peer review. The antithesis is falsified because in breach of the 3rd LOE prohibiting leaving any Socratic questions unanswered, the wise judge on the social contract with humanity must do what science failed to do and provide for instance the Gravity Angel as a historic precedent solution because claiming best practice by not taking a shot at the goal is worse than at least taking a shot. It thus doesn’t constitute a strawman fallacy. Contrary to angels; snowflakes and beehives, etcetera, are observed. Observing many life-death Nirvana movie cycles also is the least ill-founded base for any elementary model. 5th LHN FACT Part of the 3rd LOE Bayesian procedure is the operation of hypothesis, anti-thesis, and thesis as a probability having assumed something as 100% true defined as a fact. At an elementary level, facts exist in infinite non-imaginary workability is hereby mathematically proven in number salad. Facts exist even though they are not all directly completely observable. Facts pro a probandum, facts con and the temporarily established facts as a proven best practice inherent circular argument on a goal. The cat is murdered and dead or not dead, maybe attempted murder. Taking the quantum weird fact that the cat is both dead and alive at the same time is absurd and thus falsified as inconsistent because it’s a contradiction and thus proven to be anti-scientific pseudo-science on any elementary scientific claim. Having one or more elements when moving requires a volume of space.

6th LOE INFINITE SPACE There is one element of infinite 3D Euclidean empty thus non-curved space ether (an element that completely surrounds all objects) dynamically constantly invaded by elements of non-empty mass filling the 3D Euclidean volumes of dynamic elements. Euclid’s parallel postulate is proven beyond reasonable doubt as a geometric theorem as the only logical explanation consistent with all known data taken into evidence and not an axiomatic assumption taking the liberty of unreasonable doubt by any majority of peers in breach of the Order of the 4th LOE. The volume, form, and kg mass remain absolutely the same in infinity is the * only * logical solution. 6th LHN FREEDOM Taking the artistic freedom of consciously ignoring slight errors and accepting unwitting uncertainty errors to test in trial and error is a dictate of ‘The Law’. Your freedom in all aspects of “breathing space” is limited by the rules of invading mass

Abstract

“What is important for citizens to know and be able to do?” That is the question that underlies the triennial survey of 15-year-old students around the world known as the Programme for International Student Assessment (PISA). PISA assesses the extent to which students near the end of compulsory education have acquired key knowledge and skills that are essential for full participation in modern societies. The assessment, which focuses on reading, mathematics, science and problem solving, does not just ascertain whether students can reproduce knowledge; it also examines how well students can extrapolate from what they have learned and apply that knowledge in unfamiliar settings, both in and outside of school. This approach reflects the fact that modern economies reward individuals not for what they know, but for what they can do with what they know. All 34 OECD member countries and 31 partner countries and economies participated in PISA 2012, representing more than 80% of the world economy.

With mathematics as its primary focus, the PISA 2012 assessment measured 15-year-olds’ capacity to reason mathematically and use mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena, and to make the wellfounded judgements and decisions needed by constructive, engaged and reflective citizens. Literacy in mathematics defined this way is not an attribute that an individual has or does not have; rather, it is a skill that can be acquired and used, to a greater or lesser extent, throughout a lifetime.

The PISA assessment provides three main types of outcomes: - basic indicators that provide a baseline profile of students’ knowledge and skills; - indicators that show how skills relate to important demographic, social, economic and educational variables; and - indicators on trends that show changes in student performance and in the relationships between student-level and school-level variables and outcomes.

Geographic coverage

PISA 2012 covered 34 OECD countries and 31 partner countries and economies. All countries attempted to maximise the coverage of 15-year-olds enrolled in education in their national samples, including students enrolled in special educational institutions.

Analysis unit

To better compare student performance internationally, PISA targets a specific age of students. PISA students are aged between 15 years 3 months and 16 years 2 months at the time of the assessment, and have completed at least 6 years of formal schooling. They can be enrolled in any type of institution, participate in full-time or part-time education, in academic or vocational programmes, and attend public or private schools or foreign schools within the country. Using this age across countries and over time allows PISA to compare consistently the knowledge and skills of individuals born in the same year who are still in school at age 15, despite the diversity of their education histories in and outside of school.

Kind of data

Sample survey data [ssd]

Sampling procedure

The accuracy of any survey results depends on the quality of the information on which national samples are based as well as on the sampling procedures. Quality standards, procedures, instruments and verification mechanisms were developed for PISA that ensured that national samples yielded comparable data and that the results could be compared with confidence.

Most PISA samples were designed as two-stage stratified samples (where countries applied different sampling designs. The first stage consisted of sampling individual schools in which 15-year-old students could be enrolled. Schools were sampled systematically with probabilities proportional to size, the measure of size being a function of the estimated number of eligible (15-year-old) students enrolled. A minimum of 150 schools were selected in each country (where this number existed), although the requirements for national analyses often required a somewhat larger sample. As the schools were sampled, replacement schools were simultaneously identified, in case a sampled school chose not to participate in PISA 2012.

Experts from the PISA Consortium performed the sample selection process for most participating countries and monitored it closely in those countries that selected their own samples. The second stage of the selection process sampled students within sampled schools. Once schools were selected, a list of each sampled school's 15-year-old students was prepared. From this list, 35 students were then selected with equal probability (all 15-year-old students were selected if fewer than 35 were enrolled). The number of students to be sampled per school could deviate from 35, but could not be less than 20.

Around 510 000 students between the ages of 15 years 3 months and 16 years 2 months completed the assessment in 2012, representing about 28 million 15-year-olds in the schools of the 65 participating countries and economies.

Mode of data collection

Face-to-face [f2f]

Research instrument

Paper-based tests were used, with assessments lasting two hours. In a range of countries and economies, an additional 40 minutes were devoted to the computer-based assessment of mathematics, reading and problem solving.

Test items were a mixture of questions requiring students to construct their own responses and multiple-choice items. The items were organised in groups based on a passage setting out a real-life situation. A total of about 390 minutes of test items were covered, with different students taking different combinations of test items.

Students answered a background questionnaire, which took 30 minutes to complete, that sought information about themselves, their homes and their school and learning experiences. School principals were given a questionnaire, to complete in 30 minutes, that covered the school system and the learning environment. In some countries and economies, optional questionnaires were distributed to parents, who were asked to provide information on their perceptions of and involvement in their child’s school, their support for learning in the home, and their child’s career expectations, particularly in mathematics. Countries could choose two other optional questionnaires for students: one asked students about their familiarity with and use of information and communication technologies, and the second sought information about their education to date, including any interruptions in their schooling and whether and how they are preparing for a future career.

Cleaning operations

Software specially designed for PISA facilitated data entry, detected common errors during data entry, and facilitated the process of data cleaning. Training sessions familiarised National Project Managers with these procedures.

Response rate

Data-quality standards in PISA required minimum participation rates for schools as well as for students. These standards were established to minimise the potential for response biases. In the case of countries meeting these standards, it was likely that any bias resulting from non-response would be negligible, i.e. typically smaller than the sampling error.

A minimum response rate of 85% was required for the schools initially selected. Where the initial response rate of schools was between 65% and 85%, however, an acceptable school response rate could still be achieved through the use of replacement schools. This procedure brought with it a risk of increased response bias. Participating countries were, therefore, encouraged to persuade as many of the schools in the original sample as possible to participate. Schools with a student participation rate between 25% and 50% were not regarded as participating schools, but data from these schools were included in the database and contributed to the various estimations. Data from schools with a student participation rate of less than 25% were excluded from the database.

PISA 2012 also required a minimum participation rate of 80% of students within participating schools. This minimum participation rate had to be met at the national level, not necessarily by each participating school. Follow-up sessions were required in schools in which too few students had participated in the original assessment sessions. Student participation rates were calculated over all original schools, and also over all schools, whether original sample or replacement schools, and from the participation of students in both the original assessment and any follow-up sessions. A student who participated in the original or follow-up cognitive sessions was regarded as a participant. Those who attended only the questionnaire session were included in the international database and contributed to the statistics presented in this publication if they provided at least a description of their father’s or mother’s occupation.

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

ABSTRACT Defining the optimum points for installing of a cable logging system is a problem faced by forestry planners. This study evaluated the application of a mathematical programming model for optimal location of cable logging in wood extraction. The study was conducted in a forestry company located in Parana State, Brazil. We collected data during timber harvesting and developed mathematical models to define the optimal location of the cable logging considering the variables “cycle time” and “extraction distance”. The variable “cycle time” affected the definition of the optimal location of equipment resulted in a reduced number of installation points with the largest coverage area. The variable “distance extraction” negatively influenced the location, with an increased number of installation points with smaller coverage. The developed model was efficient, but needs to be improved in order to ensure greater accuracy in wood extraction over long distances.

The study of disorders of consciousness (DoC) is very complex because patients suffer from a wide variety of lesions, affected brain mechanisms, different severity of symptoms, and are unable to communicate. Combining neuroimaging data and mathematical modeling can help us quantify and better describe some of these alterations. The goal of this study is to provide a new analysis and modeling pipeline for fMRI data leading to new diagnosis and prognosis biomarkers at the individual patient level. To do so, we project patients’ fMRI data into a low-dimension latent-space. We define the latent space’s dimension as the smallest dimension able to maintain the complexity, non-linearities, and information carried by the data, according to different criteria that we detail in the first part. This dimensionality reduction procedure then allows us to build biologically inspired latent whole-brain models that can be calibrated at the single-patient level. In particular, we propose a new model inspired by the regulation of neuronal activity by astrocytes in the brain. This modeling procedure leads to two types of model-based biomarkers (MBBs) that provide novel insight at different levels: (1) the connectivity matrices bring us information about the severity of the patient’s diagnosis, and, (2) the local node parameters correlate to the patient’s etiology, age and prognosis. Altogether, this study offers a new data processing framework for resting-state fMRI which provides crucial information regarding DoC patients diagnosis and prognosis. Finally, this analysis pipeline could be applied to other neurological conditions.

ABSTRACT The goal of this study was to define an empirical model to calculate the leaf area in rice from linear leaf measure in genotypes used by farmers in Brazil. Through the leaf dimensions it is possible to identify the final crop yield from the LAI. Therefore, the leaves shape is closely related to the production of photoassimilates that will be converted into grain yield. Field experiments were carried out in four counties of Rio Grande do Sul with twelve-three varieties of rice in four growing seasons. We measured the length and width of leaves to construct the model. The relationship between leaf area and linear dimensions was shaped using a linear model for each genotype, and general model grouping all genotypes. The model accuracy was measure following statistics: Root Mean Square Error, BIAS, modified index of agreement and coefficient r. The non-destructive method for individual leaves was appropriate for estimating the leaf area in rice. Moreover, the general equation was estimated and can be used for all modern genotypes of rice in Brazil.

Variation in bacterial composition inside a host is a result of complex dynamics of microbial community assembly, but little is known about these dynamics. To deconstruct the factors that contribute to this variation, we used a combination of experimental and modeling approaches. We found that demographic stochasticity and stationary heterogeneity in the host carrying capacity or bacterial growth rate are insufficient to explain quantitatively the variation observed in our empirical data. Instead, we found that the data can be understood if the host-bacteria system can be viewed as stochastically switching between high and low growth rates phenotypes. This suggests the dynamics are significantly more complex than logistic growth used in canonical models of microbiome assembly. We develop mathematical models of this process that can explain various aspects of our data. We highlight the limitations of snapshot data in describing variation in host-associated communities and the importance of using time-series data along with mathematical models to understand microbial dynamics within a host.