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]]>October 29, 2018 6.38am EDT

http://theconversation.com

Test scores, school report cards and Facebook posts complaining about homework problems often drive critiques of how math is taught in schools.

Amid the debates, it has become increasingly clear that one ingredient is necessary for success: opportunities for students to talk about math. Unfortunately, these are often lacking in U.S. classrooms.

We are both math education researchers. While we focus on different levels of the K-12 span, a common theme across our work is the role of talk in math classrooms – what talk can sound like, how talk impacts student learning, and how teachers can support math talk.

Want to support your student’s understanding of math? Talking will play a critical role. And a good place to start is to talk about math yourself.

For some educators and researchers, learning math means coming to know and use terms and procedures in order to quickly solve problems. Others may prioritize learning the range of ways to solve a given problem. Others, still, point to the value of skills to solve problems that may come up in “the real world.”

Those are all important aspects of mathematical proficiency, but we believe that learning to communicate about the subject is an equally important goal.

By “math talk,” we mean sharing, analyzing and making sense of math. Students might discuss their strategies for solving a problem, explaining not only what they did but also the reasoning behind their work. They can also make observations, pose questions and express uncertainties.

It’s also key for students listen to their peers – to understand what they did and respond with a comment or question. In the process, disagreements or errors might emerge. These are not things to avoid; rather, they are opportunities to extend learning. Engaging in math talk helps all involved understand the ideas at hand.

Research, such as the work led by education researchers Suzanne Chapinand Beth Herbel-Eisenmann, has shown how math talk supports learning. It can improve memory and understanding; aid the development of language and social skills; and boost confidence and interest in math.

Learning math is not a process of acquiring a set of facts or procedures, but a process of becoming one who participates in a community that does mathematical work. People use math to collaborate and communicate with others. They make sense of problems that are interesting and complex. They justify their ideas and work to convince others of the validity of those ideas. They make sense of the justifications posed by others to understand, critique and build on their thinking. These skills are not reserved for mathematicians or engineers, but apply to wide range of careers.

The classroom in which math talk is not supported is a familiar scene: desks in rows, a teacher presenting a new procedure, and students working individually, focused on copying problems, getting an answer, and doing so as quickly as possible.

There are many ways in which a teacher can foster a classroom rich in opportunities for math talk. One recommendation, from research in cognitive science, is the use of “worked examples” – problems that have been worked out by someone else, perhaps a hypothetical student – to improve student learning. For example, students can be presented with two different but correct strategies to a problem and be asked to compare and contrast them, looking for the benefits and drawbacks of each approach. As a class, students can compare their ideas and raise new questions, all facilitated by the teacher.

But math talk is not just something that can happen in a classroom. In our positions, we each often get asked by friends and family about how to help their children in math. Our answer? Talk more about math – and preferably not just about homework assignments.

Math can be found in anything in ways that are appropriate for different ages. Say you are out shopping: How many people are in the store? How high is the ceiling? How many beach balls would it take to fill up the room? How do you know? Taking the time to engage with your student around any of those questions is math talk.

Many of these questions might not have a readily available answer, and that can be a good thing. Talking about what you would need to know or do to find an answer is just as valuable, and likely even more valuable, than time spent with flash cards and apps with math “games” that only focus on speed with procedures. Blogs and social media have become spaces to share the ways in which you can be “talking math with your kids” (#tmwyk on Twitter).

Whether in second grade or in an AP calculus classroom, mathematics achievement will continue to lag without value placed on math talk.

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]]>**BBC NEWS: January 29, 2019**

**B**You’ll find it on the wall of nearly every school chemistry laboratory in the land.

And generations of children have sung the words, “hydrogen and helium, lithium, beryllium…” in an attempt to memorise some of the 118 elements.

This year, the periodic table of chemical elements celebrates its 150th birthday.

The United Nations has designated 2019 as the International Year of the Periodic Table to celebrate “one of the most significant achievements in science”.

In March, it will be 150 years since the Russian scientist, Dmitri Mendeleev, took all of the known elements and arranged them into a table.

Most of his ideas have stood the test of time, despite being conceived long before we knew much about the stuff that makes up matter.

On Tuesday, the year will be officially launched in Paris. So, what’s so special about this iconic symbol of science?

Dr Peter Wothers of the University of Cambridge is an expert on the subject.

He thinks if aliens came down to Earth, this flag of science would not have escaped their attention.

“Would an alien have a periodic table?” he says.

“I think they probably would, because it is something that is absolutely fundamental – this is not just some creation of humans, there is something innate and fundamental to this – there’s chemical law, physical law behind this.”

**The laws of chemistry**

Mendeleev (1834-1907) created his early periodic table in 1869. He took the 63 known elements and arranged them into a table, mainly by their atomic mass.

Although he wasn’t the first to do this, his interpretation involved a leap of ingenuity, in that he put those with similar properties below each other into groups and left gaps for new elements to be slotted in.

“People had been doing that for some time – but finally there was some natural basis – or some law – that meant they needed to be arranged in some way,” says Dr Wothers.

One hundred and fifty years on, there have been fundamental shifts in our understanding of matter.

“Obviously Mendeleev at the time knew nothing about the sub atomic structure of the atom, so he was going on only the atomic weights, which weren’t necessarily determined to the right accuracy at the time,” says Dr Wothers.

After the discovery of protons, scientists realised that the atomic number of an element is the same as the number of protons in its nucleus. Thus, in the modern periodic table, the elements are arranged according to their atomic number – not their relative atomic mass.

“We now know the ‘how it works, why it works’, and this is to do with quantum mechanics and the arrangements of electrons in atoms and so on,” he says.

There are now more than 100 elements, laid out in order of increasing atomic number. There are repeating patterns in the properties of the elements, which give the periodic table its name.

Elements with similar properties are arranged to form columns (groups).

The periodic table is now a thing of both beauty and practical use, says Dr Wothers.

“You can understand certain things just by considering the place of an element in this table, or in this arrangement, that’s why it’s so useful to chemists.”

This year, which has been designated the International Year of The Periodic Table, may also represent its heyday.

Currently, the seventh period of the periodic table has been completed, with the recent addition of four elements in December 2015.

This has made it “quite whole and beautiful”, he says.

“At the moment – this very year – I think we are very privileged, because the periodic table is in its most perfect form, ” says Dr Wothers.

“And probably the most perfect form it will ever be in.”

People are currently working on synthesising heavier elements, and, if they manage the task, the periodic table will change yet again.

“As soon as just one more is discovered, then we’ll have to start a row – the eighth period,” he says.

“And then it will lose some of its beauty, because the eighth period will never be completed I think it’s fair to say.”

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