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Features of photomath ai, ai-powered problem solver, the core feature is an advanced ai algorithm capable of solving a wide range of mathematical problems, from basic arithmetic to complex calculus equations., step-by-step explanations, for each solved problem, the tool provides detailed step-by-step explanations, helping users understand the process and learn how to solve similar problems on their own., handwriting recognition, the tool can recognize handwritten problems, allowing users to take pictures of their handwritten math problems and receive instant solutions and explanations..
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Softening the sharp edges in mathematics.
For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start â to approach the subject with playfulness and curiosity, not anxiety or dread.
âMost people have only ever experienced what I call narrow mathematics â a set of procedures they need to follow, at speed,â Boaler says. âMathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.â
âMathematics should be flexible, conceptual, a place where we play with ideas and make connections," says Professor Jo Boaler. (Photo: Robert Houser Photography)
Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced âHow to Learn Math,â the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users.
In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls âishingâ a math problem can help students make better sense of the answer.
What do you mean by âmath-ishâ thinking?
Itâs a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport â these are generally answered with what I call âishâ numbers, and thatâs very different from the way we use and learn numbers in school.
In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. Theyâre given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 â but the most common answer 13-year-olds gave was 19. The second most common was 21.
Iâm not surprised, because when students learn fractions, they often donât learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.
But donât you also risk sending the message that mathematical precision isnât important?
Iâm not saying precision isnât important. What Iâm suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, theyâll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.
Some people ask me, âIsnât âishingâ just estimating?â It is, but when we ask students to estimate, they often groan, thinking itâs yet another mathematical method. But when we ask them to âishâ a number, they're more willing to offer their thinking.
Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mind-set. I think we all need a little more ish in our lives.
You also argue that mathematics should be taught in more visual ways. What do you mean by that?
For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things â all of that contributes to our understanding of how it works.
Thereâs an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubikâs Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking.
Some years back we were interviewing students a year after theyâd done that activity in our summer camp and asked what had stayed with them. One student said, âIâm in geometry class now, and I still remember that sugar cube, what it looked like and felt like.â His class had been asked to estimate the volume of their shoes, and he said heâd imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.
When we learn about cubes, most of us donât get to see and manipulate them. When we learn about square roots, we donât take squares and look at their diagonals. We just manipulate numbers.
I wonder if people consider the physical representations more appropriate for younger kids.
Thatâs the thing â elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school itâs all symbolic. Thereâs a myth that thereâs a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.
Click to enlarge: A depiction of various ways to calculate 38 x 5, numerically and visually. (Image: Courtesy of Jo Boaler)
Thereâs an example in the book where youâve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldnât it be easier to teach students one standard method?
That narrow, rigid version of mathematics where thereâs only one right approach is what most students experience, and itâs a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, theyâre not developing number sense. They donât learn how to use numbers flexibly in different situations. It also makes students who think differently believe thereâs something wrong with them.
When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, itâs powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.
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A great tool to help students learn new things, prepare for tests, and master subjects like math, chemistry, and physics. Unlike traditional tutoring services, our app doesn't just hand out answers - it guides students through each problem with detailed step-by-step explanations and solutions, empowering them to understand and solve similar problems on their own. Here's how our app helps you learn: Comprehensive help with homework. Whether you're solving algebraic equations or balancing chemical reactions, our app will give you the support you need to solve even the most challenging problems. Our application will help you cope with even the most complex tasks! Easy organization: With the ability to save completed tasks and questions in the app's file directory, students can easily return to their work to review, share it with classmates, or print it for reference. Cooperative Learning: Need more help? AI Homework Helper facilitates group learning by allowing users to work on math problems with friends, classmates and others, creating a collaborative learning environment. For those looking for unlimited access to our premium features, we offer a subscription service: Your iTunes account will be charged upon confirmation of purchase. Subscriptions are automatically billed according to the selected plan. Manage your subscription and turn off auto-renewal in Settings to maintain control of your membership. Subscriptions with a free trial period will transition to a paid subscription upon renewal. At AI Homework Helper we believe in empowering students to become confident and independent learners. Try our app today and discover the difference it can make in your academic journey. Privacy Policy: https://docs.google.com/document/d/1_5xd-bfOv8_3y3huQ64q0-NcKNFlpJT6aLiqrel15VI/edit Terms of Use: https://docs.google.com/document/d/1ceeWBb2GMjoYEs9gEVAnEIYgN1T0G7F-DCNWoiSrvYU/edit
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Here's how: 0 1. Input Your Math Problem. Type the math problem into the input box or upload an image of the math problem. Alternatively, input the problem into our math calculator. 0 2. Let Mathful Formulate a Solution. Our math AI or math calculator will work to generate a detailed, accurate solution to your math problem. 0 3.
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Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed, a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries.In 2013 Boaler, a former high school math teacher, produced "How to Learn Math," the first massive open online course (MOOC) on ...
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