## Sunday

### What's Math Got To Do With It? - Chapter 4

Chapter 4:  Taming the Monster

I definitely enjoyed chapter 4. The chapter discusses one of our favorite topics - testing.

A few statements that Boaler makes in the chapter are:
* American children are tested more than ever and more than students in the rest of the world.
* The tests used in the U.S. are rejected by most other countries.
* Tests are damaging to schools, teachers, and students - to their health, hearts, and minds.
* It's hard to find any multiple choice questions used in Europe or in any national assessment, in any subject, at any level. (I've always taken multiple choice tests - I had no idea they are not used everywhere!  Anyone from a different country reading this - what are your tests like??) (Anyone in U.S. - are your tests mostly multiple choice?)

Boaler identifies reasons not to use multiple choice tests:
1) Multiple choice testing is known to be biased.
2) Timed multiple choice tests cause anxiety.
3) The best thing a multiple choice test shows is the ability to complete a multiple choice test.
4) Using questions that are not multiple choice allows teachers to better assess student understanding, which includes the thinking that the student does and expresses in words, numbers, and symbols. If students are simply choosing a correct answer, this information won't be available.

According to Boaler, tests in most states are extremely narrow - they don't assess thinking, or problem solving. Instead, they assess the use of procedures. She states that in the U.S., math teachers must focus on teaching what will be tested, rather than on what students need to know for work or for life. What about you? Do you agree with this statement in regards to your school/class?

Boaler states that with the Common Core era, free-response items will replace some multiple-choice items (on the state tests my students take, we've had multiple choice with several free-response for quite a long time now-before Common Core).

The results of standardized tests label students as low achievers, or "below average," and help to create low-achieving students; the label destroys their confidence and gives them the identity of a low-achiever. Research reveals that confidence in one's ability to succeed in math in an intrinsic part of success and motivation.

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Boaler identifies "assessment for learning" as an alternative to the traditional "assessment of learning." This is a form of assessment that gives useful information to teachers and parents, but also allows students to take charge of their own learning. Assessment for learning is based on the idea that students should have:
1) A clear sense of exactly what they are learning (the concept - not the page number or chapter title):
Students have math goals to work toward - details about important concepts and how they are linked. These should be clear statements that express what students should be understanding. The example Boaler gives is, "I have understood the difference between mean and median and know when each should be used." Boaler cites an interesting study that showed great gains in low-achieving students whose class used this approach; it concluded that the students had previously been unsuccessful not because of a lack of ability, but because they hadn't known what they were supposed to be focused on.
2) Where they are in the achievement of mastery. Students can show their self-assessment by putting red, yellow, or green stickers on their work; teachers can use red, yellow, or green cups for students to display. Boaler does note that students in research studies were hesitant to show red to begin with. However, after "green cup" students were asked to explain their understanding, students who didn't understand became more willing to show red.
3) What they need to do to be successful. Teachers need to give constructive feedback about student work, rather than just giving a score. Boaler shares research that indicates that giving a grade can actually reduce achievement because the focus becomes the grade rather than what needs to happen for the student to improve. (Grades are fine at the end of the semester or term, she says). She relates this to coaching athletes - athletes aren't given grades; they are given advice and coaching to become better.

"Assessment for learning transforms students from passive receivers of knowledge to active learners who regulate their own progress and knowledge and propel themselves to higher levels of understanding."