#### The best thing we can teach students is to be quantitatively literate, think flexibly, and creatively solve problems.

What’s Math Got to Do with It? is an approachable overview of the state of the education system in the US and the current research underway to improve it. She writes in depth about many of the issues facing educators and students in our classrooms, and specifically focuses on the quality of math education and her solutions to improve it. An overview of the major issues is below along with teacher and classroom takeaways to move math education in a more positive direction.

###### International Rankings

Benchmarking on international assessments, the United States is 36^{th} out of 64 countries and drops even lower when accounting for education spending. This statistic serves to show that we must improve our math education system.

###### Impact on College Completion

Math can be a major obstacle to a college degree. Students who graduate from our public schools need to enroll in remedial math classes upon entering college; once in these classes, some are unable to pass the class. These students then do not continue on to graduation. As college degrees become more and more important in our current economy, we must recognize the impact of our K-12 math classrooms have on the future prospects of our students.

###### Standardized Testing

The testing culture of the US is unlike any other in the world. Here, students are tested on multiple choice standardized tests, sometimes in every subject in every grade of school. There are months of instruction time devoted to testing. In Europe, it would be hard to find multiple choice tests anywhere – in any subject, at any level, in any country. These tests provide little information about how individual students can improve and consequently narrow the curriculum taught in schools to what can be tested in this format.

###### Tracking

Tracking students into different math courses has a number of negative effects. Research has shown it has a negative impact on both students placed in high and low tracks. For students placed in the low tracks, they are not given the opportunity to learn at high levels, and therefore do not engage in challenging work and achieve at high levels. For students in high tracks, the pressure to perform can negatively impact their performance and facilitate a fixed mindset. Students are often placed in tracks as early as 4^{th} grade, and the earlier students are tracked, the harder it is to correctly identify student capability. The result is highly unequal schooling with a lifelong impact.

###### Two Types of Math

Students view the math they learn in school as distinct and different from the math they encounter outside the classroom. Students see math as a boring subject filled with rules, where the creative and colorful math they encounter outside the classroom isn’t even recognized as such. In passive learning classrooms, students view their role as one of memorizing procedures, they don’t consider the big ideas and connections or need to reason as part of their math learning. Instead of thinking creatively and independently about a problem, students feel they need to remember the hundreds of rules they have practiced at the expense of common sense, that rules must be followed at all costs. This is reinforced when real world pseudo contexts are introduced in word problems. Students asked to answer questions without actually using real world knowledge see math as further disconnected from the world outside the classroom walls.

#### Teacher Takeaways

- Math is about seeing and expressing relationships and ideas in numerical, graphical, symbolic, verbal, and pictorial forms.
- Researchers find the most important factor in academic success is the “opportunity to learn.” If students are not given opportunities to learn challenging and high level work, then they do not achieve at high levels.
- The idea that only some children can be successful at math or that math is a ‘gift’ that some children have and others do not is an extremely damaging myth.
- Math classrooms influence the ideas students have about themselves and other people, ideas formed about potential based on performance. Schools should teach students subject knowledge and understanding, but also have a responsibility to teach students to be open-minded, thoughtful, and respectful of others.
- Students who are not taught to flexibly use numbers often cling to methods and procedures they are taught, believing each method and procedure is equally important and must be remembered and reproduced. They also have difficulty compressing ideas; focusing on memorizing different methods, stacking one new method on top of the next. Our brains can only compress concepts, not rules or methods. The math these students are learning is more difficult. These students need to be taught to use numbers flexibly and how to think about math concepts, not labeled as low achieving and put into classes where they repeat methods over and over again.
- Students need to engage, do, act, perform, and problem solve, not memorize; if they don’t use math as they learn it, they will find it very difficult to do so in other situations.
- Students should be talking through methods and problems to fully understand them. There is a big difference between seeing something and repeating problems just as shown and being able to use the method in a different context later.
- When students discuss mathematics, they realize math is a subject they can have their own ideas about. Additionally, students who are talking gain a deeper understanding through explaining their work and the ones listening are given greater access to understanding.
- Assessment for learning gives information to teachers, parents and others, but also empowers students to take charge of their own learning. It tells students where they are, where they could be, and what they need to do to get there. It gives students motivation and power over their learning.

#### Classroom Strategies

- Mathematical goals should be outlined for students instead of a list of concepts, this helps them see the important ideas and their connections.
- Students should have a full and clear sense of what they are learning, aware of their progress, and what they have to do to be successful.
- To encourage students to be aware of their own progress toward learning goals, one option is to use traffic Lighting – red, orange, or green sticker next to work or three paper cups to show understanding of concept. Students who show green stickers or cups are then asked to help explain to others.
- For mixed ability classes to work well, two critical conditions must be met: 1) students must be given open work that can be accessed at different levels and taken to different levels and 2) students are taught to work respectfully with each other.
- Peer assessment, students judging each other’s work against clear criteria, can be a powerful learning tool because students often communicate in easily understood ways. This also provides greater access to understanding for all students.
- Diagnostic, comment-based feedback sans score is the most powerful assessment feedback in promoting learning and should be the standard way of reporting student progress.