1. Mathematics classrooms can be restrictive spaces in which not every child is afforded an opportunity to be successful in mathematics, as traditional mathematics instruction typically privileges dominant notions of mathematics while implicitly dismissing the diverse knowledge, culture, and language of all students.
2. The four Rights of the Learner (RotL), developed by bilingual teacher Olga Torres, proposes that students are entitled to each of the following rights EXCEPT:
A. The right to claim a mistake
B. The right to be understood
C. The right to speak, listen and be heard
D. The right to write, do, and represent only what makes sense
3. Valenzuela (2010) suggested that schools have both implicitly and explicitly silenced and devalued the voices of too many students while focusing on the few who can readily navigate the existing system, in a process known as “diminished schooling.”
4. Which of the following is an accurate statement about convergent and divergent formative assessments in mathematics?
A. Divergent types of formative assessment typically accept or elicit knowledge that strictly aligns with the teacher’s expectations, which creates inequities in the classroom by pushing students’ nuanced strategies to the background
B. Teachers who move toward convergent formative assessments welcome disagreement, confusion, and mistakes as a part of the learning process
C. Teachers who use convergent formative assessment provide feedback to students that is exploratory, provisional or provocative, prompting further engagement rather than correcting mistakes
D. Divergent formative assessment encourages teachers to explore the vast and nuanced landscape of students’ mathematical thinking
5. When students engage in problem-solving that lacks an obvious answer or strategy, they have more opportunities to develop connections between old and new knowledge, and if teachers design and present problems that are open-ended, students can engage in productive struggle as they actively consider the solution to the problem.
6. According to the author, which of the following is NOT one of the likely results of giving students the right to write, do, and represent what makes sense to them?
A. Students are encouraged to find multiple ways in which to justify their thinking and solution strategies
B. When students have an opportunity to represent what they know first, students’ existing knowledge is pushed to the forefront, which can promote productive discussions among students and teachers
C. Teachers can exercise their right to be informed when they encounter unfamiliar student strategies
D. Through student work, teachers elicit and make sense of students’ mathematical thinking and begin to see themselves as mathematical thinkers when they are willing to struggle through student strategies they do not understand
7. Mistakes in mathematics should not be avoided but instead valued as glimpses into students’ thinking at that moment, and children should be given a safe space to share their confusions and errors and to have their thinking valued by the teacher.
8. Using the RotL in mathematics teaching encourages the use of formative assessment as a tool to elicit the ways children know, use, and learn mathematics, and to encourage teachers to push to the forefront the students’:
A. Knowledge and creativity
B. Assets and resources
C. Innovation and perseverance
D. Abilities and interests
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