https://intensiveintervention.org/resource/what-should-we-consider-when-teaching-students-math-difficulty
Formative vs Summative
Formative assessment is when the cook tastes the soup as she is preparing it.
Summative assessment is when the guests taste the soup.
Types of Formative Assessment
The answer to the question "Why are we learning this?" is built into authentic experiences and tasks, in which students learn and do things that real people outside of school learn and do. Authentic experiences are generally more challenging and engaging for students, and the resulting learning is better remembered and more readily transferred to new situations.
Shellard and Moyer (2002) identify three critical components: “Teaching for conceptual understanding, developing children’s procedural literacy, and promoting strategic competence through meaningful problem-solving investigations.”
Find a balance between procedural and Conceptual.
A mathematics lesson cannot succeed if the other elements of teaching—classroom management, a logical progression of lessons, an effective use of assessment, and time management—are not in place.
In effective classrooms, teachers:
Demonstrate acceptance of students’ divergent ideas.
Influence learning by posing challenging and interesting questions.
Project a positive attitude about mathematics and about students’ ability to “do” mathematics.
Effective instructional techniques include:
Students are actively engaged in doing mathematics.
Students are solving challenging problems.
Interdisciplinary connections and examples are used to teach mathematics.
Students are sharing their mathematical ideas while working in pairs and groups.
Students are provided with a variety of opportunities to communicate mathematically.
Students are using manipulatives and other tools.