1. Welcome to KindergartenParent Math Morning! 2. The Coke Problem How will the length of string wrapped oncearound the can compare to the cansheight? Will it be taller, shorter, or about the samelength as the height of the can? 3. Traditional Math InstructionVersusA Constructivist Approach 4. Traditional MathematicsInstruction: Students are expected to passivelyabsorb mathematical structuresthrough repetition. Teaching consists of transmitting setsof established facts, skills, and conceptsto students. 5. Unfortunate Outcomes ofTraditional MathematicsTeaching: Children see learning mathematics aslearning procedures to be memorized. Children have difficulty solving problemsthat vary from the math they havememorized, or that require a solution paththat is previously unknown. 6. What was yourmath class like whenyou were a child?(Turn and talk to a neighbor) 7. Problem solving will bethe New Basicsof the twenty-first century-Lucy West 8. Constructivism: Knowledge is actively constructed orinvented by the child, not passivelyreceived from the environment. Ideas are made meaningful when childrenintegrate them into their existing structuresof knowledge. 9. Constructivist Teaching: Poses tasks that bring about conceptualmathematical understanding in students. Values the childs own intuitive mathematicalthinking as it gradually becomes more abstractand powerful. Takes place in an environment that is conduciveto student discussion, reflection, and sense-making. 10. Sorting Blocks by TheirAttributes Choose a card and look for attributeblocks that match the card. Identify an attribute of your own and sortthe blocks according to that attribute. 11. Attribute Look Fors Are students able to focus on a particularattribute to the exclusion of others? Can they discover other attributes besidesthe card given? (open problem-solving) Do they use language to identify theblocks? (edge, angle/corner, straight line,flat, thin/thick, color, shape, etc.) 12. Racing Bears Object of the game is for a partner team to collect 10 buttons in all. When your bear lands on a button, you and your partner take andkeep that button. Use either a three counting dice or a six counting dice, or two sixcounting dice for a challenge. Roll the dice and move your bear that number of spaces. Take turns rolling the dice and moving any bear. Try to land on abutton. You can split up the amount on the dice, and move more than onebear. Try different strategies so you can collect the buttons with the fewestnumber of moves. 13. Racing Bears Math Look-Fors(Constructivism in action) Do students recognize dot patterns? Do they move the correct number of spaces? (one-toone counting correspondence) How do students choose which bear to move? (are theyfiguring out how many more spaces a bear has to go-subtractinginformally) Are students choosing to move multiple bears during oneroll of dice? (Are they adding informally?) 14. Break the Train Work in teams of two Each student in the team creates a repeating colorpattern using snap cubes. The pattern must repeat atleast three times. Students trade trains and try to identify each otherspattern. Students break the train of each others pattern byseparating the pattern units into cars of the train. Students color in the different patterns on an activitysheet. 15. Break the Train Math Look-Fors(Constructivism in action) Are students able to identify the unit of a pattern?(algebraic). Can students reconstruct the pattern train once theyhave broken it apart? Are students able to construct/predict an AB pattern? Are students able to construct/predict a more complexpattern such as AAB, ABBA? Students can transfer their color pattern to an AABabstract pattern by writing letters for a challenge. 16. InvestigationsKindergarten CurriculumNumber and OperationsCounting and Quantity: Developing an understanding of the magnitude andposition of numbers Developing the idea of equivalenceWhole Number Operations: Using manipulatives, drawings, tools, and notation toshow strategies and solutions Making sense of and developing strategies to solveaddition and subtraction problems with small numbers 17. InvestigationsKindergarten CurriculumPatterns and Functions Repeating patterns: Constructing, describing, andextending repeating patterns Repeating patterns: Identifying the unit of a repeatingpatternData Analysis Sorting and classifying Carrying out a data investigation Representing data 18. InvestigationsKindergarten CurriculumGeometryFeatures of shape: Describing, identifying, comparing and sorting two and threedimensional shapes Composing and decomposing two and three dimensional shapes 19. Investigations KindergartenCurriculumMeasurement Understanding length Understanding length and using linear measurements 20. Getting Back to the CokeProblem: Is the string longer, shorter, or the samelength as the can? Is there a way to make sense of thisproblem? Is this a problem that has noclear solution pathway? 21. Constructing Math Sense Students who have had extensive experience with theproperties of circles will have constructed the knowledgethat a circles circumference is a little over three times itsdiameter. So if you look at the top of the Coke can and imagineabout three times the diameter, the string would belonger than the cans height. This understanding of pi goes beyond the merememorizing of a formula. 22. Memorizing ProceduresVersus Making Sense ofMathematics Students who construct their ownunderstanding of the relationship betweencircumference and diameter are betterequipped to apply this knowledge tonon-routine problem-solving situations. 23. Traditional or Constructivist?Which type of teaching would betterprepare you child for the world today? 24. Formula for pi(aproximately 3.14)