Differences might relate to what operations the students can use or what size numbers they can handle, or they might involve, for example, what meanings of an operation make sense to the students. Â are ideal for combined grades settings, since they address big math ideas that are common to side-by-side curricula. This volume includes key changes that will make it easier for teachers to use in all quality state standards environments, including direct links to Common Core content standards and standards for mathematical practice. Once they falter, they assume they will continue to falter and may simply shut down. For example: Asking for Similarities and Differences.
There may be differences in the complexity of their application, but the big ideas remain constant. I work with districts, whole school staffs, with school-based learning teams, in classrooms and with parents in an effort to promote mathematical thinking. Once the developmental differences have been identified, the object is to develop similar enough contexts for the various choices that common questions can be asked of the students as they reflect on their work. They worry that students will not make appropriate choices. Differentiating instruction in mathematics is still a relatively new idea. One set of parallel tasks might be: In this case, common follow-up questions could be: Is your object really big or not so big? How would your answer have changed if one more student was not in a classroom? Guidance for using follow-up questions to create a rich math classroom. The following fundamental principles should be kept in mind when developing new questions and tasks: All open questions must allow for correct responses at a variety of levels.
She roots her approach to differentiation in building a coherent mathematics curriculum around the big ideas of mathematics. In the first case, a student does not know whether what is desired is a definition for the term, a distance, or something else. Any question that is too specific may target a narrow level of understanding and not allow students who are not at that level to engage with the question and experience success. Now math education expert Marian Small cuts through the difficulties with her explanation of how to differentiate with two powerful and universal strategies across all math content: Open questions and Parallel tasks. Curriculum coherence requires a focus on interconnections, or big ideas. Book Features: Chapters organized around Common Core headings. Knowing that they have the choice of task should alleviate any frustration students might feel if they struggle initially.
Carole Our math classrooms are more and more diverse each year. Thus, it is important for teachers to employ strategies that will optimize the effectiveness of follow-up discussions to benefit students at all developmental levels. Some differences will be cognitive—for example, what previous concepts and skills students can call upon. Differentiation requires a different approach, one that is facilitated by teaching to the big ideas. An essential tool for every K—8 math classroom, the Open Questions for the Three-Part Lesson: Number Sense and Numeration books are organized around expectation clusters from the Ontario curriculum and include questions for the different parts of the three-part lesson.
Other students might be asked to work at a pictorial or even symbolic level with a broader range of fractions, where numerators and denominators might be multiplied or divided to create equivalent fractions and more challenging questions are asked e. Reference Marian Small Good Questions can be very useful guide, and reference marian small good questions play an important role in your products. Common follow-up questions could be: How do you know that most of the students were left? Operations, measurement, proportional thinking and patterns are featured in this calendar of problems. Follow-up discussions play a significant role in cementing learning and building confidence in students. They demonstrate that quite different forms of feedback from the teacher are needed to support the individual students. Students might approach the task in very different ways. For example, instead of asking for two numbers that add to 100, a teacher could ask for two numbers that add to something close to 100.
Continued attention to big ideas in math. Strategies for Creating Parallel Tasks. Overall, Small has created a resource that can be utilized all year by any teacher of math in the elementary and middle grades. How many students are left in the school? For example, the teacher could ask how the number 85 is like the number 100 and how it is different. Teachers may find it challenging at first to incorporate the core strategies of open questions and parallel. If students in a classroom differ in their readiness, it is usually in terms of the specifics and not the big ideas. Consider, for example, these two questions, each of which might be asked of a whole class, and think about how the results for each question would differ: If the student does not know what a fact family is, there is no chance he or she will answer Question 1 correctly.
Showing teachers how to get started and become expert with these strategies, Small also demonstrates more inclusive learning conversations that promote broader student participation. The teacher will recognize that some students need additional help and will provide as much support as possible to those students while the other students are working independently. This approach differs, in an important way, from asking a question, observing students who do not understand, and then asking a simpler question to which they can respond. She shows teachers how to start and become expert with these strategies. The teacher could allow the less developed students to explore the concepts using whole numbers while the more advanced students are using decimals. In other words, the task is in the appropriate zone of proximal development for the entire class.
Organized by topic and structured in problem sets of 5 or more, this simple to use teacher resource includes 210 mathematically important questions to engage your students in deep thinking. Students can be asked to create a sentence that includes certain words and numbers. She also demonstrates more inclusive learning conversations that promote broader student participation. How many students are on both buses? Now math education expert Marian Small cuts through the difficulties with her explanation of how to differentiate with two powerful and universal strategies across all math content: Open questions and Parallel tasks. Â The latter is no small task! Angelita draws a picture of the cupboards, the shelves, and the boxes and counts each box. Zone of proximal development is a term used to describe the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers Vygotsky, 1978, p. Replacing a Number with a Blank.
An open question is designed to ensure that many answers are good answers and will be equally valued. If students repeatedly select an easier task than they are capable of, they should simply be allowed to complete the selected task. Why might someone add to answer the question? Could you hold it in your hand? Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners. A student might realize that both numbers are said when skip counting by 5s, both are less than 200, and both are greater than 50, but only one is a three-digit number, only one ends with a 5, and only one is greater than 90. Small's approach is enhanced by skillful questioning by the classroom teacher. Teaching tips and task variations.