A Math Fair is a non-competitive problem solving event that gives teachers an opportunity to have their students do problem solving with a particular goal in mind. The math fair can be adapted to almost any curriculum and set of standards, and it will motivate and inspire all of the students. Below we have added ‘good problems’ for teachers and students to use for Math Fairs and general classroom use.
Differentiated instruction is commonly believed to be critical to improving the quality and efficiency of teachers' instructional repertoires (Fischer & Rose, 2001; Tomlinson, 2004). Tomlinson (2000) describes differentiation in four domains: content, process, product, and learning environment. Content differentiation involves varying instructional topics, for example, that students within a classroom would receive. Process differentiation involves teaching different students at different levels of difficulty. Product differentiation involves assigning different tasks to different students. Learning environment differentiation includes using different instructional groupings for students or clustering students based on ability. The purpose of this paper is to present a measure of instructional differentiation derived from teacher checklist data and apply it in the context of a randomized experiment that is part of a phased rollout of Diagnostic Assessment Tools statewide in Indiana.
Primary grade students enter the mathematics classroom with a range of differences including students' mathematical readiness, mathematical conceptions, interests, and learning profiles. Addressing the learning needs of students is not a trivial task, but accounting for these needs is essential for supporting students as they continually work toward their potential. The philosophy of differentiated instruction provides a framework for addressing the diversity of students' needs. One unique way of differentiating instruction is by incorporating differentiated educational games into the mathematics curriculum. Although the education market contains scores of mathematics games, few incorporate substantive elements of differentiation. This article presents a guide for modifying a traditional game into a differentiated mathematical game that can be used in primary classrooms. The game design and implementation described in this article were used in a research study, "Project Parallax" (principal investigators Catherine Brighton and Tonya Moon). During this study, teachers used curriculum (developed by "Project Parallax") as a vehicle for identifying mathematical promise in heterogeneous primary classrooms, and differentiated mathematical games were developed as part of the curriculum.
This article describes one teacher's efforts at creating a differentiated mathematics program in her multi-age first- and second-grade classroom. The author describes challenges encountered and successes met in this process, as well as the structures she uses to meet a variety of student abilities, including open-ended problem-solving tasks, tiered tasks, and spiraling-scaffolded tasks. Through these structures, she is able to offer students opportunities for problem-solving, development of fact fluency, and direct instruction in algorithms. Although the author acknowledges that greater differentiation is expected in multi-age settings, she makes the case that traditional graded classrooms could and should make use of a differentiated approach, suggesting that math curriculum guides should be developed to help teachers make differentiated programs a reality.
Elementary school teachers in Seattle, Washington, are encouraged to adapt differentiated instructional practices in math to accommodate the particular students in their own classrooms. Seattle Public Schools is a large, urban district serving 47,000 students who speak over a hundred languages. More than a third receive free or reduced lunch. The Everyday Mathematics curriculum developed by the University of Chicago School Mathematics Project has been the core math program for the district's elementary schools since 2007. During the 2008-2011 school years, the district funded a sizable cadre of school-based math coaches who coordinated with district-based math coaches. Differentiated instructional practices began to spread throughout classrooms in the district, not because the district imposed a predetermined instructional practice but because coaches facilitated teachers in learning from one another's differentiated practices. Being in classrooms daily, math coaches noticed some effective settings in which students of all achievement levels--including those who traditionally had not been successful--were making great strides in mastering math. The teachers in these classrooms had developed their own strategies for differentiating math instruction so that every student was supported in progressing from his or her present level of understanding to a much higher level. Because coaches from across the district met regularly to share and learn from one another, news of these teachers spread throughout the coaching cadre and then to teachers in schools that had math coaches. This article focuses on two classrooms that spurred much of the differentiation throughout the district and how the district supported teachers' efforts.
Modern classrooms are often comprised of a heterogeneous student population with varying abilities. To address this variance, third-grade teachers implemented researcher-designed, pre-differentiated, and enriched math curricula in algebra, geometry and measurement, and graphing and data analysis. The goal of the curricula was to provide academic rigor for all students, including students with high abilities. These units prompted educators to recognize learning differences in their classrooms and provide appropriate lessons for each group. Qualitative analyses revealed the treatment teachers' successful use of preassessments and grouping practices to accommodate students in their academically diverse classrooms. This study demonstrated the value of pre-differentiated and enriched curricula and professional development. Treatment teachers discussed how important it was that the curricula provided preassessments for each unit, and most lessons provided tiered activities directly connected to students' preassessment performance. Providing teachers with more meaningful and cohesive tiered activities will support teachers' efforts in academically challenging students of all levels.
In this article, the authors introduce a scenario identifying an elementary school special education teacher and interventionist (Mr. Powers) and his concerns in meeting the Common Core State Standards in Mathematics (CCSS-M). Like many teachers, Powers uses a response-to-intervention (RTI) framework to provide supports for students who require additional instruction and more intensive interventions to master curriculum standards. Wondering how he could support understanding and use of content and practice standards embodied in the CCSS-M while attending to students' unique strengths and weaknesses is addressed with a three step approach that includes: (1) Problem Identification; (2) Analyzing the Problem; and (3) Implementing a Solution. To intensify instruction for students with and without disabilities, teachers need a process to diagnostically assess students' current levels of understanding of mathematical concepts, determine areas of priority, conceptualize instructional tasks, and monitor performance. This article offers ongoing and robust diagnostic assessments to plan and implement evidence-based interventions and resources that address specific conceptual or procedural gaps in knowledge for individual students. This framework also guides teachers and interventionists to identify the problem or concern for students in terms of their mathematics understanding, analyze why the problem is occurring, implement a plan to address the problem, and evaluate if the plan is resulting in increased student performance.
This publication provides research-based guidance for intensifying instruction in reading and mathematics for students with significant learning difficulties, including students with disabilities, in kindergarten through grade 12. The guide gives technical assistance providers and states information reflecting "best practices" for implementing intensive interventions to improve education practices for struggling students, including those who receive special education. It can also be used as a resource for instructional specialists and special education teachers who are searching for broad guidelines on the design and delivery of intensive interventions. With those goals in mind, the authors present a brief review of the research on intensifying instruction for struggling students. Specifically, they discuss: (1) integrating strategies that support cognitive processes (e.g., self-regulation and memory) with academic instruction and aligning this instruction with learner needs; (2) differentiating instructional delivery by making it more explicit and systematic and by increasing opportunities for feedback; (3) increasing instructional time; and (4) reducing group size. The guide includes the following resources: (1) practice guidelines (in the form of questions and answers) that can inform the design and delivery of intensive interventions; (2) example lessons (see the Appendix) that illustrate the intensification of key areas of instructional delivery (i.e., making lessons more explicit and systematic and increasing the opportunities for student response and feedback); and (3) a list of resources for further reading and extended learning. Although this guide is not a comprehensive review of the literature, it does offer guidelines for instructional decision-makers on adapting and modifying instructional practices to deliver appropriate, responsive instruction for students with learning difficulties. Example Lessons are appended. (Contains 1 table and 1 footnote.)
Response to intervention (RTI) is a framework in which interventions are implemented mostly in general education classes to resolve academic difficulties and help to mitigate contextual variables (i.e., lack of instruction, socio economic status, cultural differences, etc.) as an explanation for academic failure. The implementation of evidence-based interventions is very important to the RTI framework. There is limited research regarding RTI and evidence-based interventions in mathematics and young students. For math interventions to be successful in an RTI framework, comprehensive math interventions have to incorporate computation fluency, problem solving, and the use of visual representational simultaneously. Moreover, early instruction in math skills sets the foundation for developing higher order math skills. Therefore, this manuscript reviews the literature regarding math interventions that would apply to early childhood students and are conducive to the RTI model
Connections to real-life applications, such as the planting and growing of corn, shape the learning experiences of the children of a rural community of Santa Avelina in the Highlands of Guatemala, so that they gain both a solid understanding of mathematics and the relevance it plays in their lives.
Field trips are wonderful opportunities to expand student learning, but the bus rides can be challenging. Perched in the first row, teachers attempt to guide the driver while tossing repeated reminders of safe bus behavior to the students in back, inevitably arriving at the destination flustered and possibly nauseated. In this article the author describes how she and her colleagues addressed the issue of stressful bus rides by focusing their second-grade studies closer to home, within walking distance of school. They developed a series of units integrating science, social studies, math, and literacy around the single focus of our local river. They begin their yearly river unit by collecting questions students have about the river. Some of the things students would like to know typically include: Where does the river start? Where does it end? Where does it come closest to our school? These questions launch a mapping unit that culminates in their first engineering design challenge: Create a tool to measure length, width, or depth of the river. As students design, construct, test, and improve their tools, they build a deep understanding of the challenges and rewards of the engineering process. They learn how to collect, analyze, and evaluate data and gain a greater understanding of the issues encountered while trying to create a map or model of a particular location. This design challenge engages students in conversations about what it means to be "measurable" and encourages them to examine what is "measurable" about a river. This guided-inquiry activity also promotes collaboration and sets the tone for a year of hands-on exploration with real-world applications. This article describes the design activities in detail as they evolved over a period of five years. It provides a model for teachers in the elementary grades who wish to replicate the process in their own settings.
Because of the pressure to increase test scores in reading and mathematics, content areas such as social studies are being eliminated from many elementary schools' curricula. It is critical that teachers find ways to integrate social studies into reading and mathematics. Social studies and mathematics may not immediately come to mind when considering subject area integration; however, these content areas can be effectively integrated through the use of children's literature and engaging activities. Research supports both curriculum integration and the use of children's literature in all content areas. Teachers must use effective methods for weaving subject areas together in ways that will motivate students and cover required state standards. This activity is an example of an activity that teachers can use to integrate social studies and math through the use of children's literature.
Interactive scenarios such as Playing to win (Probability), Saving and credit (compound interest), Population growth (exponential growth), Home decorating (geometry), Cooking by the numbers (ratios and proportions), Universal language (numbers are cross-cultural),
Teachers have the opportunity to capitalize on a vast array of real-world, two- and three-dimensional objects as they guide students in developing a conceptual understanding of geometric shapes. An important component of the NCTM Standards is to use teaching methodologies that engage children in making real-world connections to the mathematics concepts they are learning. .. became the foundation for the authentic geometry unit that first and second graders from Grace B. Luhrs Elementary School experienced, in which they became active participants in discovering geometric shapes that are part of their real-world surroundings...
There is great variety in the numerous mathematical lesson ideas that can arise from browsing through the newspaper. Since they depict recent, topical material that is constantly changing, newspapers provide an endless supply of new ideas with each new day. In this article, the author provides numerous suggestions as to how the newspaper can be used in mathematical lesson planning.
Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers help people answer many questions, including "How much?" "How fast?" and "Where do I go?" Expert teacher Bob Krech shares strategies for teaching real-world math.
To master measurement, elementary school students need opportunities to discuss how they measured and applied their developing skills and reasoning in context. When measurement is taught without a context, students may struggle to make sense of the numbers and units involved. iSTEM (Integrating Science Technology Engineering in Mathematics) authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.
students use manipulatives, engage in problem-solving activities, listen to children's literature, and use technology to experience firsthand how these instructional strategies might benefit their own students. In this article, the author discusses the Math-Box project in which teacher candidates were given the chance to present and reflect on math lessons that include the use of children's literature and manipulatives.
the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative materials. Perry and Howard used Hynes' definition of manipulatives as "concrete models that incorporate mathematical concepts, appeal to several senses and can be touched and moved around by students." The authors' definition for a mathematics manipulative material is an object that can be handled by an individual in a sensory manner during which conscious and unconscious mathematical thinking will be fostered. In this article, the authors revisit the use of mathematics manipulative materials in primary and, in Western Australia, designated middle schools. They look at the different types and the ways in which they are used by teachers
In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other classrooms.