麻豆传媒入口

Jo Boaler has spent a lot of time thinking and writing about anxiety鈥攎ath anxiety, in particular鈥攁nd its impact on kids鈥� learning trajectories.

Mathematics, she writes in her 2019 book, Limitless Mind: Learn, Lead, and Live Without Barriers, is the subject 鈥渨ith the most damaging ideas held by teachers, students, and parents.鈥� It鈥檚 one of the few academic subjects in which multitudes of students, early on, decide they鈥檙e not cut out for it: We鈥檙e either a 鈥渕ath person鈥� or we鈥檙e not. That notion tends to stick well into adulthood. 鈥淚t is difficult to know how many people walk around in society harboring damaging ideas about their math ability, but I estimate it to be at least half of the population,鈥� she writes.

Boaler, a professor of mathematics education at Stanford University, a best-selling author, and the cofounder of the math education site , has spent decades thinking about how to undo the damage. Her work, closely aligned with Stanford psychology professor Carol Dweck鈥檚 research on growth mindset, explores what Boaler calls 鈥渙ur most harmful and persistent ideas about innate ability.鈥� She鈥檚 a vocal proponent of changing the way we assess mathematics and modernizing the math curriculum鈥攅specially in high school鈥攕o that it鈥檚 more engaging, more inclusive, and more likely to prepare kids for the modern workforce.

Critics argue that by insisting on math as a joyful, creative exploration, we鈥檙e , and that by reducing or eliminating memorization and math drills, for example, we鈥檙e setting kids up for a lack of mathematical fluency. But Boaler that she鈥檚 got no quarrel with things like math facts and that teachers should help kids develop these鈥攏ot by 鈥渆mphasizing facts for the sake of facts, or using timed tests,聽but by encouraging students to use, work with, and explore numbers,鈥� a process that ultimately builds critical number sense and reinforces math facts in a more organic way.

I sat down with Boaler recently for a Zoom discussion about mathematical freedom, anxiety-producing teaching practices, and the systemic changes she says are critical for modernizing math curricula.

Sarah Gonser: In your book Limitless Mind, you say that learning is about identity. Can you explain?

Jo Boaler: Well, we know that when people learn, it鈥檚 not just about an accumulation of knowledge; it鈥檚 really about changing who they are as people.

And we鈥檝e found over the years that the traditional approach to teaching maths鈥擨鈥檓 just going to show you methods; you鈥檙e going to accept them and use them鈥攊s incompatible with the identities kids want, particularly around adolescence. Kids want to have their own ideas; they want to be respected as thinkers; they don鈥檛 want to just be given information that they simply reproduce.

They see it as a subject area where they can鈥檛 be their full selves, and it鈥檚 a large part of why people drop out of maths.

Gonser: It鈥檚 also a subject that causes a lot of very real anxiety. Why is that?

叠辞补濒别谤:听I would say it comes from a few different things: It鈥檚 a subject that is heavily tested; it鈥檚 a subject that鈥檚 often taught as right and wrong answers; and there are these widespread myths that you鈥檙e either born as a math person or you鈥檙e not. Somehow, you have the right brain, or you don鈥檛.

There鈥檚 lots of micromessaging in classrooms that might get kids to think they can鈥檛 be successful. Speed is very much at the heart of it. If you ask the class a question and then take the answer from the first kid who raises their hand, you鈥檙e sending the message that you value speed. And we know that professional mathematicians are not fast; they鈥檙e some of the slowest thinkers.

Finally, we have stereotyped ideas about who can be good at maths. So if you鈥檙e a woman or a person of color, you鈥檙e dealing with that pressure. If you have fixed ideas about who can do maths, a fixed mindset, then that stereotype can really take root.

Gonser: So how can we slow it all down and avoid making math class a place of stress and anxiety?

Boaler: I think a big part of it is A for L鈥擜ssessment for Learning鈥擨 just think that鈥檚 so critical. It changes the whole culture of classrooms for kids.

If we assess kids by giving them diagnostic feedback, not grades, and ask them to do their own reflection so that they鈥檙e able to see themselves progress on this journey鈥攅verything changes when assessment is like that in classrooms.

But we also want to change the way content is taught. Kids don鈥檛 need lots of short questions with one method and one answer. It can be open聽questions that students think about creatively and visually.

Gonser: You鈥檙e also an advocate of encouraging struggle and mistakes in classrooms. In Limitless Mind, you describe high achievers who work 鈥渁t the edge of their understanding, making mistake after mistake in difficult circumstances, correcting mistakes, moving on and making more mistakes.鈥� In the classroom, why is that important?

Boaler: The best times for learning are when you鈥檙e struggling and finding things difficult; that鈥檚 when your brain is on fire with activity. I think it鈥檚 really important to share the value of struggle with students. When I teach, I say to students, 鈥淚 want you to struggle, because that鈥檚 really good for you.鈥� I think it鈥檚 freeing for students when they know that鈥檚 a goal. And I think you should keep sharing that, reinforce it during every lesson.

It鈥檚 really going to involve changing how we assess kids. If kids take a test and they鈥檙e penalized for making mistakes, that鈥檚 a counter message鈥攁nd studies have shown that this mixed message is worse than no message at all. Don鈥檛 tell them that struggle is good if you鈥檙e going to mark them wrong when they struggle.

I think it鈥檚 important that we always let kids resubmit work. And if you鈥檙e using grading鈥擨鈥檓 not a fan of grading myself鈥攂ut if students don鈥檛 do well the first time, to allow them to work on it again sends a great message that learning and struggle are valued.

Gonser: Let鈥檚 talk about broader, more systemic curricular changes. You鈥檙e a prominent voice in the conversation about re-sequencing math curricula so that it鈥檚 more than a gateway to higher-level mathematics. What鈥檚 changed in our world to make this so urgent?

Boaler: Well, we need to modernize not just how we teach it, but the actual content we鈥檙e teaching in classrooms. The content we teach in maths was created around the 1800s and really hasn鈥檛 changed since then. It was created at a time when we needed kids to be calculators. And so learning arithmetic, calculating things quickly鈥攖hat was important.

But the world has changed dramatically. In high school, in particular, we鈥檙e teaching a wide array of methods for kids to do by hand that they鈥檒l never use in their lives again. You will never go into a workplace and have people, by hand, go through synthetic division. So we鈥檙e spending too many hours giving kids this outdated content that they鈥檙e so turned off by. For what reason?

Gonser: What should we be teaching instead?

Boaler: So I鈥檓 very excited about bringing into mathematics. I am one of the five writers of a new framework in California where we are highlighting data science as a really important part of maths.

Now, it鈥檚 hard to do that because the Common Core Standards really didn鈥檛 include data science, and they need to聽be updated. But what we鈥檝e done is try and bring a data science perspective to the current standards. This data science initiative is very exciting, not only because it gives teachers of all grades interesting content to work with, but it also helps kids become data literate, which is something they really need in this world.

There are more data points in the world than there are stars in the galaxies right now; the world is filled with data. So even little kids need to prepare to become data literate.

Gonser: You鈥檙e also leading the charge on changing the high school math sequence, streamlining the algebra-geometry-algebra sandwich so there鈥檚 room for a data science class鈥攃an you tell me more about that?

Boaler:聽In the high school years, something very exciting is happening. For generations, really, there鈥檚 been this race to get to calculus because it can get you into college.

It鈥檚 built on a . Because there are so many courses before calculus in middle school and high school, it鈥檚 effectively meant we鈥檙e pushing kids out of the calculus track in sixth grade, which is awful. The content is also not very up-to-date and not very engaging.

There鈥檚 recently been a dramatic change in California: The UC and Cal State systems will now accept data science as a third-year course instead of Algebra 2. This is amazing and important because Algebra 2 is a course that is the end of the road for most kids, and now they can take data science instead.

Gonser: Why is Algebra 2 the end of the road for so many kids?

Boaler: Because it鈥檚 so procedural and uninteresting that the vast majority of kids, after they鈥檝e done Algebra 2, don鈥檛 take any more maths. Data science is completely different. As we鈥檙e rolling it out, we鈥檙e communicating: This can be a course in high school that any student can take. You don鈥檛 have to be advanced in middle school, and yet it can lead to a high-level STEM career. I see that completely changing who ends up going into STEM.

Gonser: What do you say to critics who argue this is a change that will water down the curriculum, make it less rigorous?

Boaler: It鈥檚 totally rigorous, actually. Mathematics is a very broad subject. There鈥檚 no reason that we should say, 鈥淟et鈥檚 just value this part, which is calculus.鈥� The mathematics of data science involves matrices and probability and statistics and linear algebra鈥攚hich is beyond what鈥檚 often taught in calculus.

Gonser: My last question comes from an 麻豆传媒入口 reader, a teacher, who asks: 鈥淲hat鈥檚 your greatest piece of advice for early math educators?鈥�

Boaler: My biggest piece of advice is to really spend time trying to change kids鈥� mindsets and ideas about themselves, because that will pay huge dividends. If you encourage struggle, if you remind kids that they can learn anything, we now know there are no limits to what people can learn.

Kids should know that if the kid next to them is solving something more quickly, it doesn鈥檛 matter. We know that kids enter school with a growth mindset, and that drops with each passing year.聽And part of that is kids looking at other kids and thinking, 鈥淥h, they can do it better than me.鈥� We have to counter those ideas and聽couple that with math that鈥檚 open and creative. When you do that, things change.