Lateo.net - Flux RSS en pagaille (pour en ajouter : @ moi)

🔒
❌ À propos de FreshRSS
Il y a de nouveaux articles disponibles, cliquez pour rafraîchir la page.
À partir d’avant-hierInformatique & geek

Les équations montrées dans les films sont-elles vraies ?

Le Théorème de Marguerite, La Voie Royale, Will Hunting ou encore Les figures de l’ombre : dans tous ces films, des équations et des calculs apparaissent à l’écran. Loin d’être écrits au hasard, ils sont généralement conçus par des consultants scientifiques, un rôle méconnu du grand public. Nous leur avons parlé.

Pourquoi calcule-t-on des milliards de décimales de Pi ?

pi-pixabay

Calculer des milliards et des milliards de décimales de Pi n'est pas fondamentalement inutile, mais l'intérêt de cette démarche est moins évident qu'il n'y paraît.

La réforme du lycée a été un désastre pour les filles en maths et en sciences

maths géométrie calcul mathématiques

Favoriser l'accès des filles aux filières scientifiques est un enjeu majeur. La réforme récente du lycée a toutefois eu un impact néfaste sur le nombre de bacheliers scientifiques. Les lycéennes en ont particulièrement souffert, révèle cet article pour The Conversation.

Quand les maths prédisent le temps

Vilhem Bjerknes est le père des équations primitives, qui modélisent l'évolution de l'atmosphère et ont fondé les prédictions météorologiques et climatologiques.

Photomath, l’app qui résout les problèmes de maths, est officiellement éditée par Google

Maths Problème

Quoi de mieux adapté qu'un ordinateur pour résoudre des problèmes de maths ? Et tout le monde a un ordinateur dans sa poche, puisque les smartphones sont bien assez puissants pour calculer les résultats des opérations les plus complexes. Reste à résoudre le casse-tête de la saisie des problèmes : Google a désormais une application dédiée.

Kalker – La calculatrice scientifique de votre terminal

Par : Korben

Quand j’étais plus jeune, on me répétait souvent : « Mais tu dois être tellement fort en maths vu ce que tu sais faire avec un ordinateur« .

Mais non, aucun rapport les anciens. Je suis mauvais en maths, c’est un fait ! Mais ça ne doit pas m’empêcher aujourd’hui de vous parler de Kalker, une calculatrice scientifique qui s’utilise dans le terminal, et qui supporte la syntaxe mathématique et la possibilité d’utiliser des variables et des fonctions de votre choix ainsi que la différentiation, l’intégration et les nombres complexes.

Avec Kalker, vous pourrez jongler avec les opérateurs les plus basiques +, -, *, /, aux opérateurs plus spécialisés comme ! pour les factorielles ou % pour les pourcentages. Vous pouvez également manipuler des groupes avec des parenthèses (), des crochets [], mais aussi utiliser des fonctions de plafond ⌈ceil⌉ et de plancher ⌊floor⌋. Sans oublier les vecteurs (x, y, z, ...) et des matrices [x, y, z; a, b, c; ...] ? La plupart de ces trucs sont du chinois pour moi, mais si vous kiffez ça, ça va vous permettre de manipuler ces structures avec la même facilité que si vous manipuliez de simples nombres sur votre calculatrice Windows.

Car oui, c’est dispo sous Windows, mais également sous Linux et macOS. Et bien sûr en ligne, car vous pouvez tester ça directement depuis votre navigateur en cliquant ici.

L’intérêt de Kalker c’est qu’il peut s’adapter à vos besoins spécifiques. Vous pouvez définir vos propres fonctions et variables, pour par exemple stocker une formule compliquée dans une fonction personnalisée et l’utiliser aussi simplement que f(x).

Maintenant je m’arrête là pour ne pas vous dire plus de bêtises, mais sachez que si vous voulez l’installer, c’est par ici que ça se passe.

Et dans le même style, mais avec le support des unités plus physiques (vitesse, monnaie, fréquence, voltage…etc. y’en a pour tous les goûts), il y a également Numbat que vous pouvez découvrir ici.

Mathematicians finally solved Feynman’s “reverse sprinkler” problem

Light-scattering microparticles reveal the flow pattern for the reverse (sucking) mode of a sprinkler, showing vortices and complex flow patterns forming inside the central chamber. Credit: K. Wang et al., 2024

A typical lawn sprinkler features various nozzles arranged at angles on a rotating wheel; when water is pumped in, they release jets that cause the wheel to rotate. But what would happen if the water were sucked into the sprinkler instead? In which direction would the wheel turn then, or would it even turn at all? That's the essence of the "reverse sprinkler" problem that physicists like Richard Feynman, among others, have grappled with since the 1940s. Now, applied mathematicians at New York University think they've cracked the conundrum, per a recent paper published in the journal Physical Review Letters—and the answer challenges conventional wisdom on the matter.

“Our study solves the problem by combining precision lab experiments with mathematical modeling that explains how a reverse sprinkler operates,” said co-author Leif Ristroph of NYU’s Courant Institute. “We found that the reverse sprinkler spins in the ‘reverse’ or opposite direction when taking in water as it does when ejecting it, and the cause is subtle and surprising.”

Ristroph's lab frequently addresses these kinds of colorful real-world puzzles. For instance, back in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. (You want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s.) In 2021, the Ristroph lab looked into the formation processes underlying so-called "stone forests" common in certain regions of China and Madagascar. These pointed rock formations, like the famed Stone Forest in China's Yunnan Province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convective flows.

Read 10 remaining paragraphs | Comments

Comment Google a fait d’AlphaGeometry un champion des mathématiques

Un système d'intelligence artificielle mis au point par Google a réussi à résoudre des exercices mathématiques grâce à une méthode inédite. Cette nouveauté est un grand pas en avant dans le travail vers les intelligences artificielles générales.

Et si Pythagore n’était pas à l’origine de “son” théorème ?

mathématique-image

Pythagore ne serait pas à l'origine de son fameux théorème. Les babyloniens, 1000 ans avant lui, avaient déjà découvert cette relation.

Et si Pythagore n’était pas à l’origine de “son” théorème ?

Polymath – Un outil révolutionnaire pour transformer votre bibliothèque de samples en fichiers MIDI

Par : Korben

Aujourd’hui, j’ai quelque chose de super intéressant à vous présenter !!

J’ai découvert cet outil incroyable baptisé Polymath qui utilise du deep learning pour transformer n’importe quelle bibliothèque musicale en une bibliothèque de samples destinée à votre production musicale.

Imaginez, vous avez une tonne de sons que vous avez récupérés à gauche ou à droite, à partir de vidéos YouTube par exemple, histoire un jour de pouvoir vous inspirer de tel ou tel petit bout. Et bien avec Polymath, il n’est plus nécessaire de fouiller dans tout ça et surtout extraire ce qui vous intéresse au format MIDI.

Polymath le fait pour nous en utilisant plusieurs réseaux neuronaux tels que Demucs, sf_segmenter, Crepe, Basic Pitch, pyrubberband et librosa. Il sépare automatiquement les morceaux en pistes (rythmes, basses, etc.), les quantifie au même tempo et grille rythmique, analyse la structure musicale, la tonalité, et d’autres informations (timbre, volume, etc.), et convertit l’audio en MIDI.

Mais avant de vous lancer tête baissée, voici comment installer et utiliser Polymath. Vous devez d’abord vous assurer d’avoir ffmpeg et python installés sur votre système.

Vous pouvez ensuite cloner le dépôt Polymath en utilisant cette commande :

git clone https://github.com/samim23/polymath

Une fois cela fait, installez les dépendances nécessaires avec la commande

cd polymath
pip install -r requirements.txt

Si vous rencontrez un problème avec basic-pitch, essayez d’exécuter cette commande :

pip install git+https://github.com/spotify/basic-pitch.git

La plupart des bibliothèques utilisées par Polymath sont compatibles avec les GPU via CUDA, alors consultez ce guide pour configurer TensorFlow avec CUDA si vous voulez.

Ensuite, pour ajouter des chansons à votre bibliothèque Polymath, utilisez simplement les commandes suivantes pour les vidéos YouTube ou les fichiers audio locaux :

python polymath.py -a n6DAqMFe97E

python polymath.py -a /path/to/audiolib/song.wav

Notez que les chansons seront automatiquement analysées une première fois, ce qui peut prendre un certain temps. Mais une fois que les chansons seront dans la base de données, vous pourrez y accéder rapidement.

Vous pourrez ensuite rechercher et quantifier des chansons similaires à un tempo spécifique, et même convertir les fichiers audio traités en MIDI (notez que pour le moment, il y a certaines limitations concernant les percussions). Je vous invite fortement à lire la documentation dispo sur Github pour apprendre à utiliser l’outil. Et y’a même la possibilité de faire tourner ce truc dans Docker. C’est fou !!

Ce qui est génial, c’est que vous pouvez ajuster divers paramètres dans Polymath pour adapter l’outil à vos besoins spécifiques. Que vous soyez un producteur de musique débutant, DJ expérimenté ou développeur spécialisé dans le machine learning audio, vous pourrez personnaliser chaque réglage afin d’extraire parfaitement les sons que vous recherchez.

C’est comme si on avait un assistant virtuel dédié à la création d’échantillons personnalisés à partir d’une bibliothèque musicale. C’est un gain de temps de dingue. Ça va sans aucun doute transformer notre façon de travailler avec la musique.

Mathesar – Une interface intuitive pour Postgres

Par : Korben

En tant que développeur, vous êtes surement à la recherche de nouveaux outils pour faciliter votre travail quotidien. Ça tombe bien puisque, je vous présente aujourd’hui Mathesar, un outil open-source (licence MIT) qui simplifie la gestion des données pour tous les utilisateurs et cela peu importe votre niveau technique.

Mathesar offre une interface web conviviale, permettant de travailler avec des données en provenance d’une base PostgreSQL dans une présentation familière puisque ça ressemble à un tableur type Excel.

Actuellement en version alpha publique, la mission de Mathesar c’est de rendre la compréhension et la manipulation de données accessibles à tous.

Mathesar offre ainsi de nombreuses fonctionnalités, dont la capacité de se connecter à des bases de données Postgres existantes, de créer et de mettre à jour des schémas et des tables, et de gérer la saisie des données.

De plus, il propose des options de filtrage, de tri et de regroupement pour manipuler rapidement les données, ainsi qu’un générateur de requêtes pour créer des requêtes sans aucune connaissance en SQL ou en jointures.

L’outil prend en charge les migrations de schéma, utilise des fonctionnalités Postgres telles que les clés primaires et étrangères, et offre des types de données personnalisés et un contrôle d’accès de base.

Si ça vous dit de tester avant de l’installer chez vous, une démo est accessible ici.

Combining computing and maths to teach primary learners about variables

In our first seminar of 2023, we were delighted to welcome Dr Katie Rich and Carla Strickland. They spoke to us about teaching the programming construct of variables in Grade 3 and 4 (age 8 to 10).

Dr Katie Rich
Dr Katie Rich
Carla Strickland
Carla Strickland

We are hearing from a diverse range of speakers in our current series of monthly online research seminars focused on primary (K-5) computing education. Many of them work closely with educators to translate research findings into classroom practice to make sure that all our younger learners have positive first experiences of learning computing. An important goal of their research is to impact the development of pedagogy, resources, and professional development to support educators to deliver computing concepts with confidence.

Variables in computing and mathematics

Dr Katie Rich (American Institutes of Research) and Carla Strickland (UChicago STEM Education) are both part of a team that worked on a research project called Everyday Computing, which aims to integrate computational thinking into primary mathematics lessons. A key part of the Everyday Computing project was to develop coherent learning resources across a number of school years. During the seminar, Katie and Carla presented on a study in the project that revolved around teaching variables in Grade 3 and 4 (age 8 to 10) by linking this computing concept to mathematical concepts such as area, perimeter, and fractions.

Young person using Scratch.

Variables are used in both mathematics and computing, but in significantly different ways. In mathematics, a variable, often represented by a single letter such as x or y, corresponds to a quantity that stays the same for a given problem. However, in computing, a variable is an identifier used to label data that may change as a computer program is executed. A variable is one of the programming constructs that can be used to generalise programs to make them work for a range of inputs. Katie highlighted that the research team was keen to explore the synergies and tensions that arise when curriculum subjects share terms, as is the case for ‘variable’. 

Defining a learning trajectory

At the start of the project, in order to be able to develop coherent learning resources across school years, the team reviewed research papers related to teaching the programming construct of variables. In the papers, they found a variety of learning goals that related to facts (what learners need to know) and skills (what learners need to be able to do). They grouped these learning goals and arranged the groups into ‘levels of thinking’, which were then mapped onto a learning trajectory to show progression pathways for learning.

Four of the five levels of thinking identified in the study: Data storer, data user, variable user, variable creator.
Four of the five levels of thinking identified in the study: Data Storer, Data User, Variable User, Variable Creator. Click to enlarge.

Learning materials about variables

Carla then shared three practical examples of learning resources their research team created that integrated the programming construct of variables into a maths curriculum. The three activities, described below, form part of a series of lessons called Action Fractions. You can read more about the series of lessons in this research paper.

Robot Boxes is an unplugged activity that is positioned at the Data User level of thinking. It relates to creating instructions for a fictional robot. Learners have to pay attention to different data the robot needs in order to draw a box, such as the length and width, and also to the value that the robot calculates as area of the box. The lesson uses boxes on paper as concrete representations of variables to which learners can physically add values.

""

Ambling Animals is set at the ‘Data Storer’ and ‘Variable Interpreter’ levels of thinking. It includes a Scratch project to help students to locate and compare fractions on number lines. During this lesson, find a variable that holds the value of the animal that represents the larger of two fractions.

""

Adding Fractions draws on facts and skills from the ‘Variable Interpreter’ and ‘Variable Implementer’ levels of thinking and also includes a Scratch project. The Scratch project visualises adding fractions with the same denominator on a number line. The lesson starts to explain why variables are so important in computer programs by demonstrating how using a variable can make code more efficient. 

Takeaways: Cross-curricular teaching, collaborative research

Teaching about the programming construct of variables can be challenging, as it requires young learners to understand abstract ideas. The research Katie and Carla presented shows how integrating these concepts into a mathematics curriculum is one way to highlight tangible uses of variables in everyday problems. The levels of thinking in the learning trajectory provide a structure helping teachers to support learners to develop their understanding and skills; the same levels of thinking could be used to introduce variables in other contexts and curricula.

A learner does physical computing in the primary school classroom.

Many primary teachers use cross-curricular learning to increase children’s engagement and highlight real-world examples. The seminar showed how important it is for teachers to pay attention to terms used across subjects, such as the word ‘variable’, and to explicitly explain a term’s different meanings. Katie and Carla shared a practical example of this when they suggested that computing teachers need to do more to stress the difference between equations such as xy = 45 in maths and assignment statements such as length = 45 in computing.

The Everyday Computing project resources were created by a team of researchers and educators who worked together to translate research findings into curriculum materials. This type of collaboration can be really valuable in driving a research agenda to directly improve learning outcomes for young people in classrooms. 

How can this research influence your classroom practice or other activities as an educator? Let us know your thoughts in the comments. We’ll be continuing to reflect on this question throughout the seminar series.

You can watch Katie’s and Carla’s full presentation here:

Join our seminar series on primary computing education

Our monthly seminar series on primary (K–5) teaching and learning is of interest to a global audience of educators, including those who want to understand the prior learning experiences of older learners.

We continue on Tuesday 7 February at 17.00 UK time, when we will hear from Dr Jean Salac, University of Washington. Jean will present her work in identifying inequities in elementary computing instruction and in developing a learning strategy, TIPP&SEE, to address these inequities. Sign up now, and we will send you a joining link for the session.

The post Combining computing and maths to teach primary learners about variables appeared first on Raspberry Pi.

Comment extraire les données d’un graphique ?

Par : Korben

En matière de logiciel, que ce soit pour Windows, macOS ou Linux, plus l’interface est moche, plus l’outil est puissant. Et là, je vous demande de vous arrêter d’aller au-delà des apparences puisque WebPlotDigitizer est un outil vraiment puissant.

Il arrive parfois qu’on récupère un graphique sans avoir les données qui ont permis sa génération. Et c’est bien dommage, car les données brutes pourraient alors être réutilisées ou reprises pour générer d’autres types de graphiques.

WebPlotDigitizer permet de reverser ce genre d’images pour en extraire tout simplement les données. L’outil est décrit comme semi-automatique. C’est-à-dire que vous devez quand même placer des repères sur le graph pour qu’il puisse se repérer et ensuite vous proposer les données brutes.

Il fonctionne avec des types de graphiques différents (XY, barres, polaires, ternaires…etc.), mais également des cartes ou des photos prises au microscope qui contiendraient une échelle. Grâce à ses algos, WebPlotDigitizer vous permettra alors d’extraire automatiquement un grand nombre de données de tous ces graphiques.

Vraiment génial pour les chercheurs, les informaticiens, les enseignants…etc.

Pour bien capter comment ça fonctionne, je vous invite quand même à regarder cette vidéo, car l’outil n’a pas une prise en main instinctive. Faut se former rapidement, mais après, ça vaut vraiment le coup.

L’outil est dispo sous macOS, Windows, Linux et même en version web en cliquant ici.

Un tuto en français est également disponible ici.

Building a maths curriculum for a world shaped by computing

In the penultimate seminar in our series on cross-disciplinary computing, we were delighted to host Conrad Wolfram (European co-founder/CEO of Wolfram Research).

Conrad Wolfram.
Conrad Wolfram

Conrad has been an influential figure in the areas of AI, data science, and computation for over 30 years. The company he co-founded, Wolfram Research, develops computational technologies including the Wolfram programming language, which is used by the Mathematica and WolframAlpha programs. In the seminar, Conrad spoke about his work on developing a mathematics curriculum “for the AI age”.

In a computing classroom, a girl laughs at what she sees on the screen.

Computation is everywhere

In his talk, Conrad began by talking about the ubiquity of computation. He explained how computation (i.e. an operation that follows conditions to give a defined output) has transformed our everyday lives and led to the development of entire new sub-disciplines, such as computational medicine, computational marketing, and even computational agriculture. He then used the WolframAlpha tool to give several practical examples of applying high-level computation to problem-solving in different areas.

A line graph comparing the population of the UK with the number of sheep in New Zealand.
Yes, there are more people in the UK than sheep in New Zealand.

The power of computation for mathematics

Conrad then turned his attention to the main question of his talk: if computation has also changed real-world mathematics, how should school-based mathematics teaching respond? He suggested that, as computation has impacted all aspects of our daily lives, school subjects should be reformed to better prepare students for the careers of the future.

A diagram indicating that hand calculating takes up a lot of time in current maths classes.
Hand calculation methods are time-consuming.

His biggest criticism was the use of hand calculation methods in mathematics teaching. He proposed that a mathematics curriculum that “assumes computers exist” and uses computers (rather than humans) to compute answers would better support students to develop a deep understanding of mathematical concepts and principles. In other words, if students spent less time doing hand-calculation methods, they could devote more time to more complex problems.

What does computational problem-solving look like?

One interesting aspect of Conrad’s talk was how he modelled the process of solving problems using computation. In all of the example problems, he outlined that computational problem-solving follows the same four-step process:

  1. Define the question: Students think about the scope and details of the problem and define answerable questions to tackle.
  2. Abstract to computable form: Using the information provided, students translate the question into a precise abstract form, such as a diagram or algorithm, so that it can be solved by a computer-based agent.
  3. Computer answers: Using the power of computation, students solve the abstract question and resolve any issues during the computation process.
  4. Interpret results: Students reinterpret and recontextualise the abstract answer to derive useful results. If problems emerge, students refine or fix their work.

Depending on the problem, the process can be repeated multiple times until the desired solution is reached. Rather than being proposed as a static list of outcomes, the process was presented by Conrad as an iterative cycle than resembles an “ascending helix”:

A helix representing the iterative cycle of computational problem-solving.
The problem-solving ‘helix’ model.

A curriculum for a world with AI

In the later stages of his talk, Conrad talked about the development of a new computational curriculum to better define what a modern mathematics curriculum might look like. The platform that hosts the curriculum, named Computer-Based Math (or CBM), outlines the need to integrate computational thinking into mathematics in schools. For instance, one of the modules, How Fast Could I Cycle Stage 7 Of The An Post Rás?, asks students to develop a computational solution to a real-world problem. Following the four-step problem-solving process, students apply mathematical models, computational tools, and real-world data to generate a valid solution:

A module from Wolfram Research’s Computer-Based Maths curriculum.
Sample module from Computer-Based Math. Click to enlarge.

Some future challenges he remarked on included how a computer-based mathematics curriculum could be integrated with existing curricula or qualifications, at what ages computational mathematics should be taught, and what assessment, training, and hardware would be needed to support teachers to deliver such a curriculum. 

Conrad concluded the talk by arguing that the current need for computational literacy is similar to the need for mass literacy and pondering whether the UK could lead the push towards a new computational curriculum suitable for learners who grow up with AI technologies. This point provided food for thought during our discussion section, especially for teachers interested in embedding computation into their lessons, and for researchers thinking about the impact of AI in different fields. We’re grateful to Conrad for speaking about his work and mission — long may it continue!

You can catch up on Conrad’s talk with his slides and the talk’s recording:

More to explore

Conrad’s book, The Math(s) Fix: An Education Blueprint for the AI Age, gives more details on how he thinks data science, AI, and computation could be embedded into the modern maths curriculum.

You can also explore Wolfram Research’s Computer-Based Maths curriculum, which offers learning materials to help teachers embed computation in their maths lessons. 

Finally, try out Wolfram’s tools to solve everyday problems using computation. For example, you might ask WolframAlpha data-rich questions, which the tool converts from text input into a computable problem using natural language processing. (Two of my favourite example questions are: “How old was Leonardo when the Mona Lisa was painted?” and “What was the weather like when I was born?”)

Join our next seminar

In the final seminar of our series on cross-curricular computing, we welcome Dr Tracy Gardner and Rebecca Franks (Raspberry Pi Foundation) to present their ongoing work on computing education in non-formal settings. Sign up now to join us for this session on Tues 8 November:

We will shortly be announcing the theme of a brand-new series of research seminars starting in January 2023. The seminars will take place online on the first Tuesday of the month at 17:00–18:30 UK time.

The post Building a maths curriculum for a world shaped by computing appeared first on Raspberry Pi.

Nerdle – Le Wordle des matheux

Par : Korben

Si vous aimez Wordle, mais que l’orthographe ce n’est pas pour vous, vous allez pouvoir vous rattraper avec Nerdle. Même concept sauf que là c’est une petite équation qu’il faut trouver.

Niveau cheminement de la pensée, on est entre les maths et le sudoku. Je vous le dis tout de suite, ce n’est pas super simple, mais c’est rigolo si vous avez le temps.

En vert, ce sont les chiffres (+ opérateurs) qui sont OK et au bon endroit. En violet, ce sont les chiffres OK, mais au mauvais endroit. Et en noir, ce sont ceux qui n’y sont pas.

C’est marrant (5 min selon moi), mais c’est à faire chaque jour pour ralentir votre Alzheimer.

À tester ici

Mathematics and programming: exploring the links

“In my vision, the child programs the computer and, in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building.” – Seymour Papert, Mindstorms: Children, Computers, And Powerful Ideas, 1980

We owe much of what we have learned about children learning to program to Seymour Papert (1928–2016), who not only was a great mathematician and computer scientist, but also an inspirational educationalist. He developed the theoretical approach to learning we now know as constructionism, which purports that learning takes place through building artefacts that have meaning and can be shared with others. Papert, together with others, developed the Logo programming language in 1967 to help children develop concepts in both mathematics and in programming. He believed that programming could give children tangible and concrete experiences to support their acquisition of mathematical concepts. Educational programming languages such as Logo were widely used in both primary and secondary education settings during the 1980s and 90s. Thus for many years the links between mathematics and programming have been evident, and we were very fortunate to be able to explore this topic with our research seminar guest speaker, Professor Dame Celia Hoyles of University College London.

Dame Celia Hoyles

Professor Dame Celia Hoyles

Dame Celia Hoyles is a huge celebrity in the world of mathematical education and programming. As well as authoring literally hundreds of academic papers on mathematics education, including on Logo programming, she has received a number of prestigious awards and honours, and has served as the Chief Advisor to the UK government on mathematics in school. For all these reasons, we were delighted to hear her present at a Raspberry Pi Foundation computing education research seminar.

Mathematics is a subject we all need to understand the basics of — it underpins much of our other learning and empowers us in daily life. Yet some mathematical concepts can seem abstract and teachers have struggled over the years to help children to understand them. Since programming includes the design, building, and debugging of artefacts, it is a great approach for make such abstract concepts come to life. It also enables the development of both computational and mathematical thinking, as Celia described in her talk.

Learning mathematics through Scratch programming

Celia and a team* at University College London developed a curriculum initiative called ScratchMaths to teach carefully selected mathematical concepts through programming (funded by the Education Endowment Foundation in 2014–2018). ScratchMaths is for use in upper primary school (age 9–11) over a two-year period.

In the first year, pupils take three computational thinking modules, and in the second year, they move to three more mathematical thinking modules. All the ScratchMaths materials were designed around a pedagogical framework called the 5Es: explore, envisage, explain, exchange, and bridge. This enables teachers to understand the structure and sequencing of the materials as they use them in the classroom:

  • Explore: Investigate, try things out yourself, debug in reaction to feedback
  • Envisage: Have a goal in mind, predict outcome of program before trying
  • Explain: Explain what you have done, articulate reasons behind your approach to others
  • Exchange: Collaborate & share, try to see a problem from another’s perspective as well as defend your own approach and compare with others
  • bridgE: Make explicit links to the mathematics curriculum

Teachers in the ScratchMaths project participated in professional development (two days per module) to enable them to understand the materials and the pedagogical approach.

At the end of the project, external evaluators measured the childrens’ learning and found a statistically significant increase in computational thinking skills after the first year, but no difference between an intervention group and a control group in the mathematical thinking outcomes in the second year (as measured by the national mathematics tests at that age).

Celia discussed a number of reasons for these findings. She also drew out the positive perspective that children in the trial learned two subjects at the same time without any detriment to their learning of mathematics. Covering two subjects and drawing the links between them without detriment to the core learning is potentially a benefit to schools who need to fit many subjects into their teaching day.

Much more information about the programme and the materials, which are freely available for use, can be found on the ScratchMaths project’s website, and you can also read a research paper describing the project.

As at all our research seminars, participants had many questions for our speaker. Although the project was designed for primary education, where it’s more common to learn subjects together across the curriculum, several questions revolved around the project’s suitability for secondary school. It’s interesting to reflect on how a programme like ScratchMaths might work at secondary level.

Should computing be taught in conjunction or separately?

Teaching programming through mathematics, or vice versa, is established practice in some countries. One example comes from Sweden, where computing and programming is taught across different subject areas, including mathematics: “through teaching pupils should be given opportunities to develop knowledge in using digital tools and programming to explore problems and mathematical concepts, make calculations and to present and interpret data”. In England, conversely, we have a discrete computing curriculum, and an educational system that separates subjects out so that it is often difficult for children to see overlap and contiguity. However, having the focus on computing as a discrete subject gives enormous benefits too, as Celia outlined at the beginning of her talk, and it opens up the potential to give children an in-depth understanding of the whole subject area over their school careers. In an ideal world, perhaps we would teach programming in conjunction with a range of subjects, thus providing the concrete realisation of abstract concepts, while also having discrete computing and computer science in the curriculum.

Woman teacher and female students at a computer

In our current context of a global pandemic, we are continually seeing the importance of computing applications, for example computer modelling and simulation used in the analysis of data. This talk highlighted the importance of learning computing per se, as well as the mathematics one can learn through integrating these two subjects.

Celia is a member of the National Centre of Computing Education (NCCE) Academic Board, made up of academics and experts who support the teaching and learning elements of the NCCE, and we enjoy our continued work with her in this capacity. Through the NCCE, the Raspberry Pi Foundation is reaching thousands of children and educators with free computing resources, online courses, and advanced-level computer science materials. Our networks of Code Clubs and CoderDojos also give children the space and freedom to experiment and play with programming and digital making in a way that is concordant with a constructionist approach.

Next up in our seminar series

If you missed the seminar, you can find Celia’s presentation slides and a recording of her talk on our research seminars page.

In our next seminar on Tuesday 16 June at 17:00–18:00 BST / 12:00–13:00 EDT / 9:00–10:00 PDT / 18:00–19:00 CEST, we’ll welcome Jane Waite, Teaching Fellow at Queen Mary University of London. Jane will be sharing insights about Semantic Waves and unplugged computing. To join the seminar, simply sign up with your name and email address and we’ll email you the link and instructions. If you attended Celia’s seminar, the link remains the same.

 

*The ScratchMaths team are :

  • Professor Dame Celia Hoyles (Mathematics) & Professor Richard Noss (Mathematics) UCL Knowledge Lab
  • Professor Ivan Kalas, (Computing) Comenius University, Bratislava, Slovakia
  • Dr Laura Benton (Computing) & Piers Saunders, (Mathematics) UCL Knowledge Lab
  • Professor Dave Pratt (Mathematics) UCL Institute of Education

The post Mathematics and programming: exploring the links appeared first on Raspberry Pi.

New Wolfram Mathematica free resources for your Raspberry Pi

We’ve worked alongside the team at Wolfram Mathematica to create ten new free resources for our projects site, perfect to use at home, or in your classroom, Code Club, or CoderDojo.

Try out the Wolfram Language today, available as a free download for your Raspberry Pi (download details are below).

The Wolfram Language

The Wolfram language is particularly good at retrieving and working with data, like natural language and geographic information, and at producing visual representations with an impressively small amount of code. The language does a lot of the heavy lifting for you and is a great way to let young learners in particular work with data to quickly produce real results.

If you’d like to learn more about the Wolfram Language on the Raspberry Pi, check out this great blog post written by Lucy, Editor of The MagPi magazine!

Weather dashboard

Wolfram Mathematica Raspberry Pi Weather Dashboard

My favourite of the new projects is the weather dashboard which, in a few quick steps, teaches you to create this shiny-looking widget that takes the user’s location, finds their nearest major city, and gets current weather data for it. I tried this out with my own CoderDojo club and it got a very positive reception, even if Dublin weather usually does report rain!

Coin and dice

Wolfram Mathematica Raspberry Pi Coin and Dice

The coin and dice project shows you how to create a coin toss and dice roller that you can use to move your favourite board game into the digital age. It also introduces you to creating interfaces and controls for your projects, choosing random outcomes, and displaying images with the Wolfram Language.

Day and night

In the day and night tracker project, you create a program that gives you a real-time view of where the sun is up right now and lets you check whether it’s day or night time in a particular country. This is not only a pretty cool way to learn about things like time zones, but also shows you how to use geographic data and create an interactive experience in the Wolfram Language.

Sentimental 8-ball

Wolfram Mathematica Raspberry Pi 8-ball

In Sentimental 8-Ball, you create a Magic 8-Ball that picks its answers based on how positive or negative the mood of the user’s question seems. In doing so, you learn to work with lists and use the power of sentiment analysis in the Wolfram Language.

Face swap

Wolfram Mathematica Raspberry Pi face swap

This fun project lets you take a photo of you and your friend and have the Wolfram Language identify and swap your faces! Perfect for updating your profile photo, and also a great way to learn about functions and lists!

More Wolfram Mathematica projects

That’s only half of the selection of great new projects we’ve got for you! Go check them out, along with all the other Wolfram Language projects on our projects site.

Download the Wolfram Language and Mathematica to your Raspberry Pi

Mathematica and the Wolfram Language are included as part of NOOBS, or you can download them to Raspbian on your Raspberry Pi for free by entering the following commands into a terminal window and pressing Enter after each:

sudo apt-get update
sudo apt-get install wolfram-engine

The post New Wolfram Mathematica free resources for your Raspberry Pi appeared first on Raspberry Pi.

❌