Hands-On Activities to Promote Student Learning and Engagement in the M(ath) of STEM

1. Hands-On Activities to Promote Student Learning and Engagement in the M(ath) of STEM John C. Uccellini, Ed.D. Mathematics Curriculum Coordinator Indiana Area School District 501 East Pike Indiana, PA 15701 juccellini@iasd.cc 724-463-8713 (ext. 120)

2. Common Core State Standards for Mathematics Standards for Mathematical Practice

3. Make Sense of problems and persevere in solving them. • Explain the meaning of the problem. • Analyze givens. • Make conjectures. • Plan a solution path. • Consider analogous problems. • Look for a simpler problem. • Monitor and evaluate progress. • Use concrete objects or pictures to conceptualize the problem. • Represent the solution using equations, tables, graphs, and data. • Solve the problem using different methods. • Explain the relationship between different solutions.

4. Reason abstractly and quantitatively. • Demonstrate the ability to decontextualize a problem symbolically. • Manipulate symbols. • Contextualize symbols in light of the original problem. • Create a coherent representation of the problem. • Attend to the meaning of the quantities involved.

5. Construct viable arguments and critique the reasoning of others. • Understand and use stated assumptions, definitions, and previously results to construct arguments. • Make conjectures and build a logical argument. • Can break problems in cases. • Can recognize and use counter arguments. • Justify their arguments. • Communicate their arguments to others. • Reason inductively. • Compare and evaluate the effectiveness of two arguments or solutions. • Distinguish between correct and flawed logic. • Use concrete referents such as objects, drawings diagrams or actions where appropriate for making age appropriate arguments.

6. Model with mathematics. • Apply the mathematics that they know to solve problems arising in everyday life. • Interpret their results in the context of the problem and reflect on whether the results make sense.

7. Attend to precision. • Be able to communicate precisely with others. • Be able to state the meaning of the symbols, formulas, etc. they choose. • Be able to measure using various measuring tools accurately and be able to state the correct units of measure for the stated problem. • Be able to calculate accurately and efficiently and express answers with a degree of precision appropriate for the problem context. • Make explicit use of definitions, axioms, theorems, etc.

8. Look for and make use of structure. • Develop the ability to discern the patterns or structures present in mathematical problems or contexts.

9. Look for and express regularity in repeated reasoning. • Develop the ability to notice the regularity of answers and results from repeated mathematical procedures. • Look for general methods for solving related problems.

10. GOOD Math Instruction = GOOD STEM Instruction “We should be focusing on children DOING math, not learning math.” Henry “Hank” Kepner, PCLM Conference Fall 2010 Conference

11. Mathematical Learning StylesImproving Achievement in Math and Science February 2004 | Volume 61 | Number 5   Pages 73-78 Creating a Differentiated Mathematics Classroom Recognizing different mathematical learning styles and adapting differentiated teaching strategies can facilitate student learning. Richard Strong, Ed Thomas, Matthew Perini, and Harvey Silver

12. Mastery Style “Students favoring the Mastery style learn most easily from teaching approaches that emphasize step-by-step demonstrations and repetitive practice. Students in this group struggle with abstractions, explanations, and non-routine problem solving. They define mathematics as proficiency in calculation and computation. “ “Creating a Differentiated Mathematics Classroom” Strong, Thomas, Perini, Silver 2004

13. Interpersonal Style “Students favoring the Interpersonal style learn most easily from teaching approaches that emphasize cooperative learning, real-life contexts, and connections to everyday life. Students in this group struggle with independent seatwork, abstraction, and out-of-context, non-routine problem solving. They define mathematics primarily in terms of applications to everyday life.” “Creating a Differentiated Mathematics Classroom” Strong, Thomas, Perini, Silver 2004

14. Self-Expressive Style “Students favoring the Self-Expressive style learn most easily from teaching approaches that emphasize visualization and exploration. These students struggle with step-by-step computation and routine drill and practice. They define mathematics primarily in terms of nonroutine problem solving.” “Creating a Differentiated Mathematics Classroom” Strong, Thomas, Perini, Silver 2004

15. Understanding Style “Students favoring the Understanding style learn most easily from teaching approaches that emphasize concepts and the reasoning behind mathematical operations. These students struggle with work that emphasizes collaboration, application, and routine drill and practice. They define mathematics primarily in terms of explanations, reasons, and proofs.” “Creating a Differentiated Mathematics Classroom” Strong, Thomas, Perini, Silver 2004

16. Learning Style Inventory (Silver & Strong, 2003). If teachers incorporate all four styles into a math unit, they will build in computation skills (Mastery), explanations and proofs (Understanding), collaboration and real-world application (Interpersonal), and nonroutine problem solving (Self-Expressive).

17. Hands-On Activities • Promotes DOING Mathematics • Allows for the incorporation of Mathematical Learning Styles • Enhances instruction in the M of STEM

18. THE NATIONAL SCIENCE DIGITAL LIBRARYwww.nsdl.org is the nation’s online library for education and research in science, technology, engineering, and mathematics. It provides free math lessons and activities aligned with the Math Common Core Standards, as well as STEM-related blogs and other free teacher resources and lesson plan ideas. Targeted for K-12 teachers, higher-education professionals, and librarians, NSDL also provides science literary maps and iTunes multimedia files.

19. STEM to STEAM to STEAMIE; 17 Great links to Promote STEM! By Michael Gorman http://www.techlearning.com/blogs/35734