At our 爆乳熟妇一区二区三区霸乳 education 爆乳熟妇一区二区三区霸乳 seminar in July, a group of 爆乳熟妇一区二区三区霸乳ers from the CAMMP (Computational and Mathematical Modeling Program) 爆乳熟妇一区二区三区霸乳 project shared their work:

• Prof. Dr. Martin Frank, Founder of CAMMP (Karlsruhe Institute of Technology (KIT), Germany).
• Assistant Prof. Dr. Sarah Schönbrodt (University of Salzburg, Austria)
• 爆乳熟妇一区二区三区霸乳 Associate Stephan Kindler (Karlsruhe Institute of Technology (KIT), Germany)

They talked about how maths already taught in secondary schools can be used to demystify AI. At first glance, this seems difficult to do, as it is often assumed that school-aged learners will not be able to understand how these systems work. This is especially the case for artificial neural networks, which are usually seen as a black box technology — they may be relatively easy to use, but it’s not as easy to understand how they work. Despite this, the Austrian and German team have developed a clear way to explain some of the fundamental elements of AI using school-based maths.

Sarah Schönbrodt started by challenging us to consider that learning maths is an essential part in developing AI skills, as: 

1. AI systems using machine learning are data-driven and are based on mathematics, especially statistics and data
2. Authentic machine learning techniques can be used to bring to life existing classroom maths concepts
3. Real and relevant problems and associated data are available for teachers to use

A set of workshops for secondary maths classrooms

Sarah explained how the CAMMP team have developed a range of teaching and learning materials on AI (and beyond) with an overall goal to “allow students to solve authentic, real and relevant problems using mathematical modeling and computers”. 

She reflected that much of school maths is set in contexts that are abstract, and may not be very interesting or relevant to students. Therefore, introducing AI-based contexts, which are having a huge impact on society and students’ lives, is both an opportunity to make maths more engaging and also a way to demystify AI.

Workshops designed and 爆乳熟妇一区二区三区霸乳ed by the team include contexts such as privacy in social networks to learn about decision trees, personalised Netflix recommendations to learn about k-nearest neighbour, word predictions to learn about N-Grams, and predicting life expectancy to learn about regression and neural networks.

Learning about classification models: traffic lights and the support vector machine

For the seminar, Sarah walked through the steps to learn about support vector machines. This is an upper secondary workshop for students aged 17 to 18 years old. The context of the lesson is an image problem — specifically, classifying the data representing the colours of a simplified traffic light system (two lights to start with) to work out if a traffic light is red or green.

She walked through each of the steps of the maths workshop:

• Plotting data points of two classes, the representation of green and red traffic lights
• Finding a line that best separates the data points of both classes
• Figuring out what best is
• Classifying the data points in relation to the chosen (separating) line
• Validating the model statistically to see if it is useful in classifying new data points, including using test data and creating a contingency table (also called a confusion matrix)
• Discussing limitations, including social and ethical issues
• Explaining how three traffic lights can be expressed as three-dimensional data by using planes

Throughout the presentation, Sarah pointed out where the maths taught was linked to the Austrian and German mathematics 爆乳无码av一区二区三区.

Learning about social and ethical issues

As well as learning about lines, planes, distances, dot product and statistical measures, learners are also engaged in discussing the social and ethical issues of the approach taken. They are encouraged to think about bias, data diversity, privacy, and the impact of errors on people. For example, if the model wrongly predicts a light as green when it is red, then an autonomous car would run through a red traffic light. This would likely be a bigger consequence than stopping at a green traffic light that was mis-predicted as red. So should the best line reduce this kind of error?

To teach the workshops, Sarah explained they have developed interactive Jupyter notebooks, where no programming skills are needed. Students fill in the gaps of example code, explore simulations, and write their ideas for discussion for the whole class. No software needs to be installed, feedback is direct, and there are in-depth tasks and staggered hints.

Learning about regression models: Weather forecasting and the toy artificial neural network

Stephan went on to introduce artificial neural networks (ANNs), which are the basis of generative AI applications like chatbots and image generation systems. He focused on regression models, such as those used in weather forecasting. 

ANNs are very complex. Therefore, to start to understand the fundamentals of this technology, he introduced a ‘toy ANN’ with one input, three nodes, and one output. A function is performed on the input data at each node. With the toy network, the team wants to tackle a major and common misconception: that students think that ANN systems learn, recognise, see, and understand, when really it’s all just maths.

The learning activity starts by looking at one node with one input and one output, and can be described as a mathematical function, with a concatenation of two functions (in this case a linear and activation function). Stephan shared an online simulator that visualises how the toy neural network can be explored as students change two parameters (in this case, weight and bias of the functions). Students then look at the overall network, and the way that the output from the three nodes is combined. Again, they can explore this in the simulator. Students compare simple data about weather prediction to the model, and discover they need more functions — more nodes to better fit the data. The activity helps students learn that ANN systems are just highly adjustable mathematical functions that, by adding nodes, can approximate relationships in a given data set. But the approximation only works in the bounds (intervals) in which data points are given, showing that ANNs do not ‘understand’ or ’know’ — it’s just maths.

Stephen finished by explaining the mutual benefits of AI education and maths education. He suggested maths will enable a deeper understanding of AI, and give students a way to realistically assess the opportunities and risks of AI tools and show them the role that humans have in designing AI systems. He also explained that classroom maths education can benefit from incorporating AI contexts. This approach highlights how maths underpins the design and understanding of everyday systems, supports more effective teaching, and promotes an interdisciplinary way of learning across subjects.

Some personal reflections — which may not be quite right!

I have been 爆乳熟妇一区二区三区霸乳ing the teaching of AI and machine learning for around five years now, since before ChatGPT and other similar tools burst on the scene. Since then, I have seen an increasing number of resources to teach about the social and ethical issues of the topic, and there are a bewildering number of learning activities and tools for students to train simple models. There are frameworks for the data lifecycle, and an emerging set of activities to follow to prepare data, compare model types, and deploy simple applications. However, I felt the need to understand and to teach about, at a very simple level, the basic building blocks of data-driven technologies. When I heard the CAMMP team present their work at the AIDEA conference in February 2025, I was entirely amazed and I asked them to present here at our 爆乳熟妇一区二区三区霸乳 seminar series. This was a piece of the puzzle that I had been searching for — a way to explain the ‘bottom of the technical stack of fundamental concepts’. The team is taking very complex ideas and reducing them to such an extent that we can use secondary classroom maths to show that AI is not magic and AI systems do not think. It’s just maths. The maths is still hard, and teachers will still need the skills to carefully guide students step by step so they can build a useful mental model. 

I think we can simplify these ideas further, and create unplugged activities, simulations, and ways for students to explore these basic building blocks of data representation, as well as classification and representing approximations of complex patterns and prediction. I can sense the beginnings of new ideas in computational thinking, though they’re still taking shape. We’re 爆乳熟妇一区二区三区霸乳ing these further and will keep you updated.

Finding out more

If you would like to find out more about the CAMMP resources, you can watch the seminar recording, look at the CAMMP website or try out their online materials. For example, the team shared a link to the jupyter notebooks they use to teach the workshops they demonstrated (and others). You can use these with a username of ‘cammp_YOURPSEUDONYM’, where you can set ‘YOURPSEUDONYM’ to any letters, and you can choose any password. They also shared their toy ANN simulation.
The CAMMP team are not the only 爆乳熟妇一区二区三区霸乳ers who are investigating how to teach about AI in maths lessons. You can find a set of other 爆乳熟妇一区二区三区霸乳 papers here.

Join our next seminar

In our current seminar series, we’re exploring teaching about AI and data science. Join us at our last seminar of the series on Tuesday, 27 January 2026 from 17:00 to 18:30 GMT to hear Salomey Afua Addo talk about using unplugged approaches to teach about neural networks.

To sign up and take part, click the button below. We’ll then send you information about joining. We hope to see you there.

The schedule of our upcoming seminars is online. You can catch up on past seminars on our previous seminars page.

The post Secondary school maths showing that AI systems don’t think appeared first on 爆乳大森しずか无码.

We are hearing from a diverse range of speakers in our current series of monthly online 爆乳熟妇一区二区三区霸乳 seminars focused on primary (K-5) 爆乳熟妇一区二区三区霸乳 education. Many of them work closely with educators to translate 爆乳熟妇一区二区三区霸乳 findings into classroom practice to make sure that all our younger learners have positive first 爆乳无码av一区二区三区s of learning 爆乳熟妇一区二区三区霸乳. An important goal of their 爆乳熟妇一区二区三区霸乳 is to impact the development of pedagogy, resources, and professional development to support educators to deliver 爆乳熟妇一区二区三区霸乳 concepts with confidence.

Variables in 爆乳熟妇一区二区三区霸乳 and mathematics

Dr Katie Rich (American Institutes of 爆乳熟妇一区二区三区霸乳) and Carla Strickland (UChicago STEM Education) are both part of a team that worked on a 爆乳熟妇一区二区三区霸乳 project called Everyday 爆乳熟妇一区二区三区霸乳, which aims to integrate computational thinking into primary mathematics lessons. A key part of the Everyday 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 concept to mathematical concepts such as area, perimeter, and fractions.

Variables are used in both mathematics and 爆乳熟妇一区二区三区霸乳, 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 爆乳熟妇一区二区三区霸乳, 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 爆乳熟妇一区二区三区霸乳 team was keen to explore the synergies and tensions that arise when 爆乳无码av一区二区三区 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 爆乳熟妇一区二区三区霸乳 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.

Learning materials about variables

Carla then shared three practical examples of learning resources their 爆乳熟妇一区二区三区霸乳 team created that integrated the programming construct of variables into a maths 爆乳无码av一区二区三区. 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳

Teaching about the programming construct of variables can be challenging, as it requires young learners to understand abstract ideas. The 爆乳熟妇一区二区三区霸乳 Katie and Carla presented shows how integrating these concepts into a mathematics 爆乳无码av一区二区三区 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.

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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳.

The Everyday 爆乳熟妇一区二区三区霸乳 project resources were created by a team of 爆乳熟妇一区二区三区霸乳ers and educators who worked together to translate 爆乳熟妇一区二区三区霸乳 findings into 爆乳无码av一区二区三区 materials. This type of collaboration can be really valuable in driving a 爆乳熟妇一区二区三区霸乳 agenda to directly improve learning outcomes for young people in classrooms. 

How can this 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 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 爆乳无码av一区二区三区s 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 and maths to teach primary learners about variables appeared first on 爆乳大森しずか无码.

“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 爆乳无码av一区二区三区s 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 爆乳熟妇一区二区三区霸乳 seminar guest speaker, Professor Dame Celia Hoyles of University College London.

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 爆乳大森しずか无码 爆乳熟妇一区二区三区霸乳 education 爆乳熟妇一区二区三区霸乳 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 爆乳无码av一区二区三区 initiative called ScratchMaths to teach carefully selected mathematical concepts through programming (funded by the Education Endowment 爆乳无码av一区二区三区 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 爆乳无码av一区二区三区

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 爆乳熟妇一区二区三区霸乳 paper describing the project.

As at all our 爆乳熟妇一区二区三区霸乳 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 爆乳无码av一区二区三区, 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 爆乳无码av一区二区三区, 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 and computer science in the 爆乳无码av一区二区三区.

In our current context of a global pandemic, we are continually seeing the importance of 爆乳熟妇一区二区三区霸乳 applications, for example computer modelling and simulation used in the analysis of data. This talk highlighted the importance of learning 爆乳熟妇一区二区三区霸乳 per se, as well as the mathematics one can learn through integrating these two subjects.

Celia is a member of the National Centre of 爆乳熟妇一区二区三区霸乳 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 爆乳大森しずか无码 is reaching thousands of children and educators with free 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳 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 爆乳熟妇一区二区三区霸乳. 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, (爆乳熟妇一区二区三区霸乳) Comenius University, Bratislava, Slovakia
• Dr Laura Benton (爆乳熟妇一区二区三区霸乳) & 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 爆乳大森しずか无码.