Tag Archives: problem solving

Doing Math…





IMG_2602What is a Noetic Challenge? According to Merriam-Webster’s website, the combined definition of these two words would translate to “a difficult task relating to intellect.” This may be true, but to a group of 13 fifth-grade math students, the term Noetic Challenge means logic puzzles, math games, and a collaborative effort to determine how many pencils make up a “gross!”

Meeting weekly with our math enrichment specialist, Mrs. Feldman, these top math students finished their successful elementary school years by competing in a national math competition. The Noetic Math program is designed to challenge students’ mathematical thinking by strengthening problem-solving skills. All Lower School math classes incorporate a variety of challenging word problems to Posnack’s already advanced math curriculum in order to prepare students for an accelerated rate of learning in mathematics. Since their introduction to Singapore Math last year, students in grades K-5 are focusing on the importance of relating math to real-world situations and identifying problem-solving strategies to tackle higher-order thinking word problems. Whether it’s preparing a shopping list to stay within a given budget, or calculating the square footage of classrooms in our new Fischer High School building, students are learning to recognize that math touches everything in their lives. Posnack students have become quite adept at using bar models and algebraic thinking to solve authentic problems with a variety of strategies and as a result, have learned that success in mathematics IS something to brag about.

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When presented with the idea of a math contest, Mrs. Feldman’s fifth-grade groups were excited at the idea of showcasing what they’ve learned. Over 24,000 students from more than 600 schools in 47 states participated in this contest, and Posnack students received commendations in the categories of participation, national honorable mention, and team winner. The celebration began with the awarding of certificates by Mrs. Feldman, followed by ice cream and the presentation of mini calculators to the fifth-grade math team. Certificates, ice cream, prizes? When I asked one student what the best part of the afternoon was, he replied, “We get to do even harder math now!” This student’s enthusiasm reminded me of the accomplished mathematician Paul Halmos who was quoted as saying, “The only way to learn mathematics is to do mathematics.”  I can honestly say that it’s been a thrill and an honor to watch these talented students “DO” mathematics.

Click here for more information on the Noetic Math Challenge and to see a complete list of national winners.


Questions, Questions, Questions…



I recently had the opportunity to participate in a math workshop covering Singapore Math strategies. I was looking forward to spending time in the classrooms of the school hosting this event to learn more about the use of manipulatives, bar modeling, etc. But what I actually witnessed was even more valuable than a lesson in problem solving.

I was listening to the teacher of a 4th grade class deliver a geometry lesson. The students were busy working with partners using dry erase boards and protractors, while cutting out and measuring triangles. I suddenly realized that the teacher wasn’t teaching in the traditional sense of the word, but rather she was leading the students by asking questions…….and more questions……..and even more questions. Even when a student answered a question, his answer was followed by yet another question such as “Suppose we didn’t know the length of the hypotenuse…?” or “What would happen if instead of being an isosceles triangle…?” When a student gave an answer that wasn’t exactly what the teacher was looking for, instead of saying they were incorrect, she asked them to explain their line of thinking. The level of engagement in the classroom was electric – I could almost see the proverbial “lightbulb” illuminate above each student’s head as the answers clicked and their “AHA” moment occurred.

What I was witnessing was an example of a constructionist approach to learning. Using this approach, students become actively involved in the learning process, and use knowledge gained from both the classroom and life experiences to apply to problem solving. These students are “constructing” their own learning experience as the teacher leads them towards self-discovery of the answers. Using this method of learning, students are also encouraged to defend their line of reasoning as the teacher poses questions that may seemingly contradict a student’s response.

From a teaching perspective, this approach is not always easy to implement. As educators, we have been trained to impart knowledge to our students. We prepare students for assessments and make sure that they are ready to take on the challenges of the next grade level. The learning goals of the curriculum are addressed and we must ensure that our students are able to demonstrate proficiency in a variety of skills.

Is it possible then to encourage students to take the lead in the learning process while still moving along the curriculum continuum? Interestingly enough, it most definitely is! Active problem solving, collaborative learning, and making connections to real-world situations, are all ways in which students not only demonstrate proficiency, but exhibit cognitive growth and the ability to use higher order thinking skills. Sure, teachers may have to modify lesson plans or adjust a pacing schedule to accommodate an extended discussion among classmates. But the lessons learned from such a discussion have the potential to create a greater and more substantive learning experience for the students.

So what lesson did I learn in that classroom last week? Admittedly, Geometry was never one of my favorite subjects. The theorems, the angles, the postulates – none of it ever really made sense as I struggled to envision how a three-dimensional model could be sketched on a one-dimensional piece of paper. But sitting in this class of 10-year-old students, I suddenly had my own “AHA” moment. Maybe it was the way the students were manipulating the shapes on their boards, or cutting along the lines of the graph paper. Maybe it was the sheer intimidation factor of being in a room of young children who exhibited confidence in their ability to converse using geometric terms in a way in which I was never comfortable. But more than likely, it was the active learning and the excitement in the classroom as everyone constructed their own answers to the presented questions. And so for me, this simple geometry lesson provided “proof” that sometimes in life, the questions are more meaningful than the answers.