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]]>Extract from Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching (Wiley, 2015 pages 190- 191) by Jo Boaler.

Mathematics is a subject that should be highlighting depth of thinking and relationships at all times. In a recent visit to China I was able to watch a number of middle and high school math lessons in different schools. China outperforms the rest of the world on PISA and other tests, by a considerable margin (PISA, 2012). This leads people to think that math lessons in China are focused upon speed and drill. But my classroom observations revealed something very different. In every lesson I saw teachers and students worked on no more than three questions across an hour’s lesson. The teachers taught ideas, even ideas that are among the more definitional and formulaic in mathematics, such as the definitions of complementary and supplementary angles, through an inquiry orientation. In one lesson, an extract of which can be viewed here: www.youcubed.org/high-quality-teaching-examples/, the teacher explored the meaning of complementary and supplementary angles with students, by giving an example and asking students to “ponder the question carefully” and then discuss questions and ideas that came up. The ensuing discussion around complementary and supplementary angles moved into a depth of terrain I have never before seen in my observations of mathematics classrooms teaching this topic. The teacher provocatively took the students’ ideas and made incorrect statements for the students to challenge and the class considered together all of the possible relationships of angles that preserve the definitions. This is an extract from a typical US lesson on complementary and supplementary angles, taken from the TIMSS video study of teaching in different countries (Stigler & Hiebert, 1999):

US example, from http://www.timssvideo.com

**Teacher:** Here we have vertical angles and supplementary angles. Angle A is vertical to which angle?

**Students chorus:** 70 degrees Teacher: Therefore angle A must be?

**Students chorus:** 70 degrees.

**Teacher:** Now you have supplementary angles. What angle is supplementary to angle A?

**Students Chorus:** B

**Teacher:** B is and so is…?

**Students:** C

**Teacher:** Supplementary angles add up to what number?

**Students:** 180 degrees

In the extract above we observe definitional questions with one answer, that the teacher is leading students towards. Compare this with one of the lessons we watched in China, in which the teacher did not ask questions such as “Supplementary angles add up to what number?” She asked questions such as: Can two acute angles be supplementary angles? Can a pair of supplementary angles be acute angles? These are questions that require students to think more deeply about definitions and relationships. Here is an extract from the lesson in China that I watched and that stands as an important contrast to the US lesson.

**Student:** As he just said if there are two equal angles, whose measures add up to 180 degrees, they must be two right angles. Because the measures of acute angles are always smaller than 90 degrees, the sum of the measures of two acute angles will not be larger than 180 degrees.

**Teacher:** Therefore, if two angles are supplementary, they must be two obtuse angles?

**Student:** That is not correct.

**Teacher:** No? Why? Teacher: I think if two angles are supplementary, they must be two obtuse angles.

**Student:** I think they could be an acute angle and an obtuse angle.

**Teacher:** She says, although they cannot both be acute angles, they can be one acute angle and one obtuse angle.

**Student:** For example, just like the Angle 1 and Angle 5 in that question. One angle is an acute angle. The other one is an obtuse angle.

**Teacher:** OK. If two angles are supplementary, they must be one acute angle and one obtuse angle?

**Student:** That’s still not accurate.

**Student:** You should say, if two angles are supplementary, at least one of them is an acute angle. Other

**Students:** No, at least one angle is larger than 90 degrees.

**Student:** An exception is when the two angles are right angles.

The lessons from the US and from China could not have been more different. In the US lesson the teacher fired procedural questions at the students and they responded with the single possible answer. The teacher asked questions that could have come straight from books, that highlighted an easy example of the angle, and students responded with definitions they had learned. In the lesson from China the teacher did not ask pre-decided questions, she listened to students’ ideas and made provocative statements in relation to their ideas that pushed upon their understanding. Her statements caused the students to respond with conjectures and reasons, thinking about the relationships between different angles.

The second half of the lesson focused on the different diagrams students could draw that would illustrate and maintain the angle relationships they had discussed. This involved the students producing different visual diagrams, flipping and rotating rays and triangle sides. Students discussed ideas with each other and the teacher, asking questions around the ideas, pushing them to a breadth and depth I had not imagined before seeing the lesson. As the class discussed the visual diagrams of angle relationships one of the students reflected: “This is fascinating”. There are not many students who would have drawn this conclusion from the US version of the lesson

download excerpt from Jo’s book download video transcript download task from video

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]]>This is one of those newsletters I really enjoy as we have new and exciting things to tell you about. Thank you to all of you who used some of our Week of Inspirational Math materials, they were downloaded one quarter of a million times! so we know they were used far and wide, which is wonderful.

First, we have made a new video for students. It is 8.5 minutes long and it shares the messages that we think are extremely important for students’ relationships with maths. Please share it with your students – and their parents – and also please share it on social media to get the messages out as widely as we can. Viva La Revolution!

Second, along with the student video we have made a new student section of our website. This is a site for students to go and watch the video whenever they want, to try some great maths tasks and to read and share inspirational stories of overcoming maths struggles.

And third, we are heading to CMC-South tomorrow and wanted to extend an invitation to youcubians who will be there, to join us in the bar on Friday night at 5 pm. Some of the youcubed team and I will gather at the Hilton Hotel out by the pool at Al Fresco, come along and say hello! We have 2 sessions at CMC-South. On Friday at 10.30 Cathy and I will share some of the work and new initiatives we are thinking about for youcubed. We would love your feedback on our ideas if you are able to come. On Saturday at 1.15 I will lead a session on the new brain science and what it means for maths classrooms.

I am excited to go to CMC South as my new book has just come out and we will have 100 copies there. I will be in the conference hall at 3pm on Friday signing books if you would like to come and buy one and get it signed.

These are exciting times and we continue to appreciate all of our youcubians who are part of the maths revolution,

Viva La Revolution,

Jo

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]]>Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don’t like math and often fail in math classes. She’s followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck’s concept of ‘mindset’ into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets:

-Explains how the brain processes mathematics learning

-Reveals how to turn mistakes and struggles into valuable learning experiences

-Provides examples of rich mathematical activities to replace rote learning

-Explains ways to give students a positive math mindset

-Gives examples of how assessment and grading policies need to change to support real understanding

Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

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]]>As you may have seen from the media coverage, last week was an exciting one for the youcubed team with the launch of Think It Up! a new education initiative. Think It Up! is being supported by the entertainment industry and big funders. Together we are working to change the antiquated ideas about education, including those about mathematics teaching and learning. You may have seen the blockbuster TV show on all the major channels on Friday night that opened with Justin Bieber and included many appeals to the public to support teachers and students. Think It Up! is asking teachers and students to plan exciting projects that will be shown to potential funders, so I encourage you to visit their website and get a project funded. Being at the live TV event was exciting, I even managed to get a photo with my 2 daughters’ favorite TV star to send home to them (see below)! Modern Family’s Cam (Eric Stonestreet) said he was sorry he only got half of Cathy!

In preparation for the live TV show our youcubed team launched 10 new pages of content on our site with all the latest brain evidence introduced and explained, youcubed.org/think-it-up/. It was quite the week in our youcubed offices as we welcomed 4 new team members – Amanda Confer, David Romano, Daniel Torres-Rangel and Estelle Woodbury – who were all thrown in at the deep end preparing a major new part of our site.

My favorite of the new posts shows us that the way we feel about ourselves, whether we believe in our own potential to grow and change – changes the way our brains react to mistakes. That is amazing and shows us the importance of self beliefs. Something that the brain evidence has shown for some time is that our beliefs are not separate from our knowledge and understanding. It is becoming clearer and clearer to me that we need to pay a lot more attention to the ways students think about math and themselves. Other posts sharing new evidence include one showing that ideas of giftedness harm students, and another showing that parents with math anxiety reduce their children’s learning but only if they help with homework. I hope you enjoy reading the new posts, and connecting with the Think it up! movement.

**Viva La Revolution,**

** Jo & the youcubed team**

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]]>David’s entire list can be found here.

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