The first Common Core mathematical practice standard emphasizes the need to have students make sense of problems and persevere in solving them.
The most important ingredient in Polya’s classic four-step problem solving strategy is the act of making decisions, as opposed to simply applying an algorithm that has been instructed.
These enrichment activities challenge students to make decisions and construct solutions – to play an active role when learning content.
Variety is favored over repetition, although care is taken to have common themes emphasized and connections reinforced.
Young adolescents have emerging cognitive powers to accompany their rapid physical growth, and math enrichment can provide middle school students with appealing opportunities to use their maturing reasoning skills. Your curriculum gave him a way to learn math that made sense to him. " - Amy, Ontario, Canada "Critical Thinking has uniquely captured the method of teaching students not only how to think logically, but to apply logic to the process of learning in every subject area.
presents math in a way that makes it not only simple to learn, but also practical to apply to everyday circumstance (obviously making math more meaningful to him)." - Katherine, Mississippi "My son hated math. [M]any companies have begun to jump on the bandwagon and produce materials that use the critical thinking label, but the contents are the same old drill and practice, and our students know the difference right away.They finish middle school and begin high school usually embarking on year-long studies of content-intensive mathematical subject areas: a year of Algebra 1, then a year of Geometry, then a year of Algebra 2, and so on.Though young adolescents begin middle school ready to think with more power, creativity, and independence, the accompanying increase in content expectations means that a balance between mathematical content and practice can be difficult to achieve.Each activity set is accompanied by needed math facts, strategy tips, and comprehensive solutions that teachers and parents can use to help support student investigations.These sorts of enrichment activities provide middle school students with an opportunity to explore mathematical content, create or reinforce ideas, make connections, and use abstract reasoning.Generally at age 11 or 12 children enter the fourth and final stage in Piaget’s four stages of cognitive development, called the formal operational stage.During this time children show significant growth in their ability to think abstractly, use advanced reasoning skills, make hypotheses and inferences, and draw logical conclusions.Note the depth and value of a critical thinking opportunity: the solution strategy connects 2D geometry with the number theory technique of factoring and is a precursor to a more sophisticated factoring procedure used in Algebra 1.The second question requires greater time investment than the first question, but is worth the extra time if one is committed to young adolescents learning content in a way that fully engages their reasoning skills.However, if mathematics education in the United States is to reach a higher standard against a worldwide benchmark, children must be encouraged to persevere with critical thinking and decision making, to embrace both the excitement and occasional frustration of authentic reasoning and creativity.The Critical Thinking Co.™ specializes in activities that stimulate use of reasoning skills and creativity when learning content.