# Using Best Practices instructional technique that are high cognitive, rigorous, and engaging

## English Language Arts

**Mathematics**

## Effective Mathematics Classroom

According to research, in an effective mathematics classroom students are engaged with important mathematics, lessons are likely to enhance students understanding and to develop students' capacity to do math successfully, and students are engaged in ways of knowing and ways of working consistent with the nature of mathematicians way of knowing and working. More specifically-

- Activity Centers on mathematical
sense making, reasoning, and understandingbyallstudents.- A carefully crafted and monitored mathematical
culture of effort and growthassures that:

- every student engages continuously in mathematical sense making, conjecturing, justifying, and/or generalizing;
- every student is developing a growth mindset, intellectual autonomy, and self-efficacy as a mathematician; and
- all students collaborate and interact in ways that show accountability to the mathematics, to learning, and to each other.
- All students engage consistently in worthwhile mathematical tasks.
- The
teacher's knowledgeof the mathematics content she/he teaches and its trajectory over time, how students learn mathematics, and how mathematicians "do math" enable the teacher to create a mathematical culture of learning and growth in which all students use worthwhile mathematical tasks as context for engaging continuously in sense making, reasoning, and understanding.-except taken from How Math Teaching Matters by Teachers Development Group

HOW STUDENTS LEARN MATHEMATICS

Students learn mathematics with depth and enduring understanding when they consistently and repeatedly (every day and every year) engage in learning experiences that emphasize:

1. Mathematically productive student-to-student discourse about their own and others’s thinking.

2. Cognitively demanding mathematical tasks that elicit high-cognitive engagement by each and every student (i.e., students justify and generalize by reasoning from and about mathematical representations and related mathematical connections, regularity, patterns, and structures)

3. Reflection and metacognition about their own and others’ mathematical thinking and disequilibrium.

4. Mathematical mistakes, stuck points, and disequilibrium as sites for new learning.

5. Adherence to mathematically productive classroom norms and relationships.

A student who learns this way from year-to-year develops a growth mindset and a powerful sense of agency and identity as a capable mathematical thinker. These research-based aspects of how students learn mathematics undergird and transcend all effective mathematics teaching and all effective mathematics professional development.

©Teachers Development Group 2017 v.2.1