MATH 391 Final Exam - Questions & Correct Answers
Constructivism ✔️Ans - Piaget; learners are not blank slates but rather
creators of their own learning; networks are added to and rearranged
throughout learning; networks are combination of constructing knowledge
and the tools for new knowledge
Sociocultural theory ✔️Ans - Mental processes exist between people in
social learning settings—learner moves ideas into his or her own
psychological realm
Two aspects of sociocultural theory ✔️Ans - -Information must be
within learners zone of proximal development
-semiotic mediation is the individual beliefs and attitudes that are affected
in sociocultural practices
Five strands of mathematical proficiency ✔️Ans - Conceptual
understanding
Procedural fluency
Strategic competence
Adaptive reasoning
Productive disposition
Conceptual understanding ✔️Ans - knowledge about the relationships
or foundational ideas of a topic
Procedural fluency ✔️Ans - Knowledge and use of rules and procedures
used in carrying out mathematical processes; symbolism
Strategic competence ✔️Ans - Attempting strategies to solve a problem
and applying different ones if they do not work
Adaptive reasoning ✔️Ans - Capacity to reflect on your work, evaluate
it, and then adapt as needed
Productive disposition ✔️Ans - Commitment to making sense of and
solving tasks, knowing that if you kept at it, you would get to a solution
, What does it mean to teach mathematics through problem solving? How
does teaching mathematics through problem solving reflect constructivism
and sociocultural theories of learning? ✔️Ans - Students learn best
through problem-solving by selecting tasks and orchestrating classroom
discourse. Teachers should pose tasks that engage students in thinking
about and developing the important mathematics they need to learn
What does it mean to orchestrate classroom discourse? What are some
important considerations in effectively implementing classroom discourse?
✔️Ans - Orchestrating classroom discourse refers to the interactions that
occur throughout a lesson. Students should be asked what strategies they
used and why; model think-alouds; critical thinking questions
Identify the 11 problem types for addition and subtractions ✔️Ans -
join: result unknown;
join:change unknown;
join: start unknown;
separate: result unknown;
separate: change unknown;
separate: start unknown;
part-part-whole: whole unknown;
part-part-whole: part unknown;
compare: difference unknown;
compare: larger unknown;
compare: smaller unknown
Make up multiplication story problems to illustrate the difference between
equal groups ✔️Ans - "Shaun has 6 bags of apples.There are 3 apples in
each bag. How many apples does Shaun have all together?"
Make up a multiplication story problem to illustrate multiplicative
comparison ✔️Ans - "Frank bought 4 pizzas. Bob bought 10 pizzas. How
many more pizzas did Bob buy?"
Create one problem as a measurement for 36/9. ✔️Ans - Jill drove 36
miles at a rate of 9 miles per hour. How many hours did it take Jill to drive
36 miles?
Constructivism ✔️Ans - Piaget; learners are not blank slates but rather
creators of their own learning; networks are added to and rearranged
throughout learning; networks are combination of constructing knowledge
and the tools for new knowledge
Sociocultural theory ✔️Ans - Mental processes exist between people in
social learning settings—learner moves ideas into his or her own
psychological realm
Two aspects of sociocultural theory ✔️Ans - -Information must be
within learners zone of proximal development
-semiotic mediation is the individual beliefs and attitudes that are affected
in sociocultural practices
Five strands of mathematical proficiency ✔️Ans - Conceptual
understanding
Procedural fluency
Strategic competence
Adaptive reasoning
Productive disposition
Conceptual understanding ✔️Ans - knowledge about the relationships
or foundational ideas of a topic
Procedural fluency ✔️Ans - Knowledge and use of rules and procedures
used in carrying out mathematical processes; symbolism
Strategic competence ✔️Ans - Attempting strategies to solve a problem
and applying different ones if they do not work
Adaptive reasoning ✔️Ans - Capacity to reflect on your work, evaluate
it, and then adapt as needed
Productive disposition ✔️Ans - Commitment to making sense of and
solving tasks, knowing that if you kept at it, you would get to a solution
, What does it mean to teach mathematics through problem solving? How
does teaching mathematics through problem solving reflect constructivism
and sociocultural theories of learning? ✔️Ans - Students learn best
through problem-solving by selecting tasks and orchestrating classroom
discourse. Teachers should pose tasks that engage students in thinking
about and developing the important mathematics they need to learn
What does it mean to orchestrate classroom discourse? What are some
important considerations in effectively implementing classroom discourse?
✔️Ans - Orchestrating classroom discourse refers to the interactions that
occur throughout a lesson. Students should be asked what strategies they
used and why; model think-alouds; critical thinking questions
Identify the 11 problem types for addition and subtractions ✔️Ans -
join: result unknown;
join:change unknown;
join: start unknown;
separate: result unknown;
separate: change unknown;
separate: start unknown;
part-part-whole: whole unknown;
part-part-whole: part unknown;
compare: difference unknown;
compare: larger unknown;
compare: smaller unknown
Make up multiplication story problems to illustrate the difference between
equal groups ✔️Ans - "Shaun has 6 bags of apples.There are 3 apples in
each bag. How many apples does Shaun have all together?"
Make up a multiplication story problem to illustrate multiplicative
comparison ✔️Ans - "Frank bought 4 pizzas. Bob bought 10 pizzas. How
many more pizzas did Bob buy?"
Create one problem as a measurement for 36/9. ✔️Ans - Jill drove 36
miles at a rate of 9 miles per hour. How many hours did it take Jill to drive
36 miles?
