4. As you enter a classroom, ask yourself this
question: "If there were no students in the room,
could I do what I am planning to do?" If your
answer to the question is yes, don't do it.
(Gen. Ruben Cubero, Dean of The Faculty, United States Air Force Academy)
5. Mathematical processes connect the
procedural to the conceptual.
Through the action of process
standards, students display their
interaction with the mathematics that
develops into a deeper understanding
for all.
(Ontario Ministry of Education, 2008)
6. Turn and Talk…
How students learn is just as
important as what students learn.
7. Experiencing Communication and Connections
Read the instructions below, then
plan your actions using the
thinking sheet provided
Make 3 cuts
2 pieces need to be of equal
length.
The other pieces need to be of
different lengths
Be prepared to prove your work.
8. If you were to place a
value or a number on
each piece, what would
they be?
Think Pair Share…
9. Communication
One of the 7 mathematical process standards
Talking and writing are critical processes which students
develop content standards.
Credit 24-7 Teacher
10. Five Productive Talk Moves…
1. Re-voicing – Repeating what students have said
and then asking for clarification
So you’re saying it’s an odd number?
2. Repeating – Asking students to restate someone
else’s reasoning
Can you repeat what he just said in your own
words?
3. Reasoning – Asking students to apply their own
reasoning to someone else’s reasoning
Do you agree or disagree and why?
4. Adding on – Prompting students for further
participation
Would someone like to add something more to
that?
5. Waiting – Using wait time Take your time …
12. Quick Write…
How did
questioning and
conversation with
this kindergarten
student reveal a
deeper
understanding ?
Classrooms that celebrate mathematical
discourse benefit both teacher and
student.
14. Jigsaw
Create a learning
environment in
which students are
encouraged to
make connections
among multiple
representations.
(NCTM, August 2010)
“Translating and moving flexibly between
representations is a key aspect of students
mathematical understanding.”
15. Round Table (also called “Round Robin”)
What mathematical operation does
this make you think of?
16. How many ways can you represent
this photo?
Use the math tools provided.
Value Line or Four CornersThe teacher presents an issue, topic, or question to the students. Then, the teacher assignsa value scale to each possible student response. For example, the teacher might introducea 1-10 Scale where 1=strong agreement and 10=strong disagreement. Students are thenasked to form a line based on how they rank their response based on the scale. Afterstudents line up, the teacher guides a discussion about the topic. After discussion,consider having the students re-evaluate where they wish to stand in the line. Analternative to value line is to ask post four answers to a question and then ask students togo to the corner that best represents their answer or perspective.
I love this quote as it really speaks to the mathematical processes and content. Math content standards are teachers teach and students learn. Math processes are how teachers teach and how students learn.Over this hour please take note that it was not planned as a sit and deliver and you sit and listen. Have you ever been to a PD where all the presenter did was read from their power point? You should never walk out from a PD valuing the PPT notes but rather the experiences and discoveries you made.
Think, Pair, ShareThink, Pair, Share, involves three components. First, each student is prompted tocomplete a task or answer a question that requires them to think. Second, each student isprompted to pair up with another student to compare, contrast or confirm the productcreated during the thinking phase. Students are also prompted to adjust their productbased on their conversation with their learning partner. Third, students are prompted toshare with the rest of the class what they have learned during the entire activity. Think,Pair, Share usually involves more complicated activities than Turn-to-your -neighbor.
Number and Shape and Space. Have the outcomes on place cards on the tables. Copy thinking sheets.
Think Pair Share
PODS
Modified Jigsaw- JigsawStudents are organized into groups with equal numbers of participants. Each group isgiven a portion of some larger task (perhaps an to read part of a chapter or part of anessay) being covered during the class. For example, six groups of students may beformed to study six different sections of a research article. Each group works to learntheir material so well that they will be able to teach it to others. After each group hasread and learned their portion of the material, the groups are reconfigured so that eachnew group has a participant from each of the previous groups. Then each memberteaches the others his or her version of the material until everyone has taught theirmaterial and all the content has been covered.
Round Table (also called “Round Robin”)Divide the class into groups and pose a question. Ask one student to write an answer ona paper and then pass paper to the person beside him or her in the group. Every studenthas a turn at answering the question. The group with the most correct answers isrecognized. Another way of doing Round Table is to have all student answer on paperand then have the group put all of their answers together with, again, the group with themost right answers being recognized. At the end of the activity, review answers,strategies, and ways of improvement.
Round Table (also called “Round Robin”)Divide the class into groups and pose a question. Ask one student to write an answer ona paper and then pass paper to the person beside him or her in the group. Every studenthas a turn at answering the question. The group with the most correct answers isrecognized. Another way of doing Round Table is to have all student answer on paperand then have the group put all of their answers together with, again, the group with themost right answers being recognized. At the end of the activity, review answers,strategies, and ways of improvement.
Value Line or Four CornersThe teacher presents an issue, topic, or question to the students. Then, the teacher assignsa value scale to each possible student response. For example, the teacher might introducea 1-10 Scale where 1=strong agreement and 10=strong disagreement. Students are thenasked to form a line based on how they rank their response based on the scale. Afterstudents line up, the teacher guides a discussion about the topic. After discussion,consider having the students re-evaluate where they wish to stand in the line. Analternative to value line is to ask post four answers to a question and then ask students togo to the corner that best represents their answer or perspective.
Graffiti… Grade One to Adult: A Cooperative Learning TacticGraffiti is a creative brainstorming process that involves collecting the wisdom of all or most of the students in the class. Method: You may wish to begin by introducing the concept of Graffiti; it helps make the process moremeaningful for studentsPlace students into groups of three or four Provide a large sheet of paper (station) for each groupEach piece of paper has a topic / question in the middle (can be same or different for each group)Students get a reasonable amount of Wait Time to think Then a specified amount of Record Time to write down their answers on the sheetThen the group stands up and goes to another station and adds their information to theinformation already there They should NOT read info already there. Duplication is irrelevant, and often can simply indicatethat info is important.The process continues until all groups have visited all stationsWhen they return, they now have the collective wisdom of the classConsiderations:Consider giving each group different coloured pens. When inappropriate comments happen, andthey do, it is easier to trace.Know how you will deal with inappropriate comments before you begin
