17 Nov General Workshop and Keynote Speech
Written by Lucía Dávila
Common Hope, Antigua, Guatemala
The teachers assumed the role of 3rd graders and were given a math task that they needed to solve with pictures and numeric representations.
The next step was to discuss with each other different approaches and solutions.
– The math goals of the task.
– Their answers and how they think their students would
– Their best guesses as to whether their 3rd,
4th, or 5th grade students would struggle with this task.
– The questions they would ask their students without telling
them the answer or how to reason toward it.
– First, the teachers were asked to read a case study
and discuss the objectives of the lesson.
– Second, the teachers did an analysis of the materials,
vocabulary, type of math problem, how the students engaged the math, teaching practices,
and the different strategies the students could have used to solve the problem.
– Next, they discussed potential struggles with such tasks
and how would they as teachers change the problem to make it more approachable.
– Also, they discussed what they would do to for
students who reached the correct solution ahead of their peers to give them
Using and connecting math representations
– Teachers shared various ways to solve the same math problem with different representations
(visual, symbolic, verbal, contextual, and physical).
– They also discussed three possible answers that students might give.
– The final topics were facilitating significant math discourse in the classroom,
students’ engagement, and the importance of asking good questions.
The teachers were divided in groups, and each received
a number corresponding to a specific “effective mathematics teaching practice.”
After some discussion time, a representative of each
group shared its conclusions with the rest of the audience. A few examples of
their insights were the following:
“To be flexible.”
“The teacher is just a guide that needs to let the students do the work and discover the knowledge by themselves.”
“Get to know your group and adapt; change your methods according to what your students need.”
“Next time I come to my classroom, I won’t only have my students’ learning as a goal, but
also for them to enjoy it.”
“Don’t be a dictator, be a facilitator.”
“Use what you already have. Be creative and use the resources around you.”
School “Colegio Agustiniano”, Guatemala City
Giving sense to the number
The math task “199+199” was given, and the teachers
had to share in pairs how they would solve it. Next, participants analyzed
divergent paths to solving the problem, remarking that they need to permit
students to choose the method that works best for them.
A math problem was presented, and the teachers had to
solve it using only pictures.
This limitation allowed teachers to have a more
physical and symbolic math experience to apply to how their students might
incorporate manipulatives to solve the same problem.
Finally, the speaker offered an array of math
representations of the problem and its solutions.
The importance of asking good questions
At the end, the speaker encouraged the teachers to pay
close attention to their verbal communication with their students. In
particular, she emphasized the importance of asking good questions to promote
math discourse in the classroom and to truly understand students’ thinking.
Visit wwww.t2t-i.org to learn more about the Effective Mathematics Teaching Practices and to get the material online.