Category Archives: For Educators

What Makes A Good Math Problem?

Good math problems value the process of using critical thinking skills by having students participate in open-ended experiences that have a clear goal but a variety of solution paths, it does not value the result or simply the right answer to a math question. Good problems should connect the mathematics students learn at school with its application in their everyday lives, making it more meaningful and relevant to the learner. By developing strategies that can be applied to new situations, good problems encourage students to reason their way to a solution among many solutions. A rich problem allows for representation of mathematical ideas and model situations, using concrete materials, pictures, diagrams, graphs, tables, numbers, words, and symbols. It also promotes the collaborative sharing of ideas and strategies by having students talk about mathematics. Since good math problems are appropriate, rich, challenging, and engaging, it should help students find enjoyment in mathematics and extend the student’s thinking by still having it relate to a key concept or big idea.

Curricular Links to the Arts

When making curricular links to the arts, big ideas need to be broad and relevant enough for students. Essential questions that provoke conceptual thinking as well as using a student’s creativity is a great place to start when thinking about integrating the arts into other subjects. In social studies, for example, questions such as: what are communities? how do they function? can take an artistic approach whereby students draw or represent what they feel a community can look like. In fact, creating a three-dimensional community integrates math, social studies, and art. When we teach social studies topics such as communities and peoples, we can ask students what they think the art looked like back then. Investigating this, then replicating the art, is invaluable and allows students to think critically by putting themselves into that time period. Students can show what they know through various drama techniques by acting out history as well.

Creating visual representations of knowledge learned in science such as drawing or acting out life cycles of the frog and butterfly, building artistic structures during science class by keeping in mind the concept of stability/forces go hand-in-hand with building/creating. Creating a song or chant to learn multiplication facts, using visual arts (sculptures and drawings) to teach geometry, are some ways to integrate art in math. Even asking students how art is used in the media can open up many discussion points. In language, students can match visual images from literature to music or dramatize storylines and poetry. Technology can manipulate and extend texts by adding images, videos, sound and hyperlinks to create new dramatic interpretations of poems. Integrating other subjects with art provides ways to explore, express, create and solve problems while encouraging inquiry-based pedagogy where students can be creative and have active roles in their own learning.

RESOURCES:

Ministry of Education – Ontario. (2009). The Ontario Curriculum: Grades 1-8 The Arts.

Upitis R. (June 2011). Arts Education for the Development of the Whole Child. Elementary Teachers’ Federation of Ontario.

Inquiry Based Learning

Inquiry Based Learning

In the Inquiry Based Learning Approach, teachers need to teach students to be flexible in the way they respond. I notice that in my classroom, there are some students who provide very simple explanations, in which case I need to prompt or encourage them to explain their thinking. Other students see the big picture, but need help clarifying their thoughts for their peers; that is why it is vital to bring everyone together to share and discuss the big ideas so that everyone learns.

Moving students from initial curiosity to regular inquiry is the big idea of inquiry based learning. It is the idea that the educator is the provocateur rather than the teacher that teaches only what he/she knows that will move learners forward into becoming more inquisitive individuals. It is OK for the teacher not to know the answers, because the learning community involves both students and teachers learning together.

As a teacher, there is not always a need to wait for the perfect question from students, because all questions are valid. Questions posed by students are meaningful to them. And those genuinely curious questions can be a good place to begin the inquiry process. Keeping a record of students’ questions is a good idea, since they offer “inquiry potential” and learners can refer to them throughout their investigations.

RESOURCES:

1. Cartier J.L. and Pellathy S.L. (April/May 2009). Integration with Big Ideas in Mind. Science and Children.

2. Ministry of Education (May 2013). Inquiry Based Learning. Capacity Building Series, Vol. 32. Retrieved from http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_InquiryBased.pdf

Self-Regulation

When students reflect on their work and decide how they are going to use the feedback given to them to improve on future tasks, they become self-regulatory and self-reflective. It is important for parents and teachers to teach children how to self-regulate by having meaningful conversations with them about what and how they are learning and what changes, if any, will they make for next time. When a child can explain what they are learning, what challenges they are facing, and what triumphs they are making, they are being critical of the knowledge that they are presented with. Asking students what next steps they are going to take next, during and after an investigation, helps the learner see that learning is ongoing and meaningful. When relevant conversations are occurring both at school and at home, students will soon realize that they must complete assignments and homework, because these activities are meant to solidify learning, and someone who is interested in their learning will ask them about the topics. Students who see the importance and relevance of learning are better at self-regulating, because they can make connections and they are reflective. To help students with this, parents and teachers need to be involved by facilitating their learning by asking questions and genuinely being interested in the topics.

Learning Goals and Success Criteria

Learning goals are endpoints/goals that students are expected to meet. They can be as big as a culminating task/project or as small as a goal for the week or an assignment that the teacher has assigned. Learning goals are important for student achievement so that learners know what is expected of them. They know what the teacher is looking for so that they remain focused and on task.

Knowing what goal to meet is important, but knowing how to get there can be daunting for many young learners. That is why it is important for teachers to create a success criteria with his/her students. Success criteria is a list of what students need to do in order to meet a set goal. For example, let’s say a learning goal is to have students be able to sort and describe polygons. A criteria for being successful at this goal may be for the students to first figure out how many sides a shape has, what its side lengths are, what angle measures it has, and what the shape’s name is. After meeting these criteria, students can steadily see that they can actually be successful at meeting the goal that is set out for them. I find that co-creating the success criteria with the students helps learners better understand what they need to do in order to accomplish what the teacher wants them to, because the criteria is worded at the learners’ level of understanding. Success criteria helps break down a big task into more manageable steps. Be sure to ask your children what learning goal they are trying to meet when they bring back homework. Chances are, they are probably working on criteria that has been introduced in class. If students have trouble explaining what goal they are trying to meet, he/she may not be making connections to help him/her solidify what is being taught. Try setting family goals with your children at home, and together, create criteria that will help the family accomplish something successfully!