Creating Mathematicians and Scientists within Young Children

1. Creating Mathematicians and Scientists within Young Children Greg Gierhart Murray State University-College of Education Dr. Nancy Lovett Regional Training Center-Calloway

2. Should Preschoolers Learn Mathematics? • Born with capabilities to solve simple numerical quantities • Possess ideas in number and geometry • Low income and minority have narrowed experiences and experience math difficulties later in life. • Brain development within the first year is significant • Brain is naturally geared to be a powerful pattern seeker • Preschoolers are intrigued to investigate shapes, measurement, the meaning of number, and how numbers work

3. Math and the Young Child • MATH IS MORE THAN ROTE COUNTING • Naturally Interested in Mathematics • It’s visible in their play and work • Teacher/Parents provide words, math experiences and resources • Explore math to scaffold understanding, Investigate size, quality, categorization, patterns, space, speed and sequence • Remember—CHILDREN VARY IN THEIR THINKING

4. Standards Standards Standards • NCTM Principles and Standards • NCTM Curriculum Focal Points • Kentucky Early Childhood Standards and Benchmarks

5. NCTM Documents Learning and Teaching Mathematics Content Strands Process Strands Reasoning Proof Communication Connections Representations Principles • Number • Geometry and Spatial relations • Measurement • Patterns/Algebra • Analyzing data • Equity • Curriculum • Teaching • Learning • Assessment • Technology

6. Preschool Teacher’s Role • Interpret what student is thinking and doing • Assess the concepts student is learning • Link concepts to the students’ experiences. Note: young children do not see the world as separate subjects—they try to link everything together—our brains do this.

7. Is Play and Work Important? Every person has a developmental need to experience creativity and self-expression People skilled at play have more power, influence, and capacity to create meaningful lives-builds problem-solving, persistence, and collaboration Play allows a conduit to new experiences, content, and meaning Play is integral to curriculum, to allow for engaging for hands-on problem solving and inspiring projects Through play, we learn to accept differences of opinion and how to resolve conflict

8. Role Play and Model Are Important

9. Research Alert Preschoolers with social and emotional problems will need to have those problems addressed before they can successfully develop their mathematical skills. • (David Sousa, How the Brain Learns Mathematics, 2008).

10. Learning Mathematics Continuum

11. Promoting Good Beginnings for Mathematics • Effective classroom approaches • Inclusion and equitable experiences for all students • Academically prepared teachers with knowledge, skills, and dispositions • Problem solving approach that uses language and communication • Using technology • Lifelong learners

12. NCTM Stand on Students Learning Mathematics • Every child is the most compelling goal! • All children (no matter race, gender, ability) should have access to Math experiences • Provide math experiences for children to be successful mathematicians • Promoting live long learners

13. MOVE SING and READ • Activating the vestibular system---brain is being told to wake up • Songs are “hooks to hang a memory on” • Read read read until you think your lips are going to fall off, and then read more

14. NCTM Stand on Students Learning Mathematics • Every child is the most compelling goal! • All children (no matter race, gender, ability) should have access to Math experiences • Provide math experiences for children to be successful mathematicians • Promoting live long learners

15. General Guidelines for Preschool Teacher to Teach Mathematics • Environment must have opportunity to explore mathematics • Recognize if math is developing or stalled in children • Plan activities that rely on mathematics (and literacy) development. • Use strategies that are meaningful and purposeful and within context • Allow students to be active participant in their learning • Embrace students thinking about mathematics by modeling and posing higher-order questions

16. Subitizing • Know the number in a set of objects without counting one to one. • Pre-requisite skill for learning counting • Strengthen this skill • Use patterns with dot cards helps • Avoid using manipulatives at first to teach this concept • Leads to understanding of addition and subtraction • Audio Input helps with Subitizing (songs)

17. Learning to Count • How many—not based on the arrangement or size • Cardinal principle needs to be reinforced • By age four-mastered counting and can apply to new situations • Once students can count using objects, next step, counting without objects

18. Counting in Other Countries • Language of other cultures logically describes the counting sequence • This helps to make sense and a deeper understanding of the base 10 system • Counting in other languages does not confuse children

19. Teacher Talk Improves Number Knowledge • Used in everyday speech influences mathematics knowledge over the school year • Questioning assists in the understanding of number and mathematics

20. Sorting and Classifying • Sorting is different from classifying • Seriation • Begins at age three and is used to understand the real world • Developmental factors to keep in mind about sorting and classfying • Age -Perceptions -Constructing Information • Tactile kinesthetic -Quantity of objects • Mathematical talking • Making it fun and offer choices

21. Levels of Sorting • Promotes understandings of relationships within a group • Increase difficulty of the sorting tasks by consideration of attributes • Level One • Level Two • Level Three • Level Four

22. Levels of Classifying • Explain their reasons behind the classification • Level One • Level Two • Level Three • Level Four • Sorting and classifying leads to grouping and regrouping which is helpful to learn math operations

23. Number and Operation Key Concepts • Counting involves learning the vocabulary of mathematics, including knowing the names of the numerals • Counting involves the ability to understand one-to-one correspondence • Counting involves the ability to understand cardinality; that the last number words said when counting a group of objects such as two, represents two things, objects, events, and so on

24. Number and Operation Key Concepts • Counting involves saying number words in a consistent, reproducible order • Counting involves abstraction: any thing can be collected together for counting • Counting involves the understanding that things can be counted in any sequence without changing the result • Counting leads to experiencing the numnber operations of adding and subtraction

25. Basic Concepts of Algebra Key Concepts: • Patterns exist everywhere in a variety of shapes, sizes, colors, numbers, and textures • It is possible to repeat and extend patterns as in music • Groups of various items may be sorted, classified, and ordered by many attributes

26. Basic Concepts of Algebra Key Concepts • The addition and subtraction of whole numbers may be represented using objects, pictures, and symbols • Addition and subtraction sentences may be constructed. “more” suggests addition, and “less” suggests subtraction • A variety of things may change in quality and in quantity

27. Basic Concepts of Geometry Key Concepts: • Geometric shapes are two- and three-dimensional • Two and three dimensional geometric shapes have multiple characteristics and properties to be analyzed • Spatial reasoning and relationships are accomplished through geometry and other representational systems

28. Basic Concepts of Geometry Key Concepts • Children’s spatial sense is their awareness of themselves in relation to people and objects around them in space. • Spatial visualization and reasoning can be used to solve problems. • Geometry describes and classifies the physical world we live in.

29. Basic Concepts of Measurement Key Concepts: • Things may be compared with respect to length, area, capacity, weight and time. • Objects may be ordered according to these attributes • Length concepts involve how long, how high, how far, and how wide

30. Basic Concepts of Measurement Key Concepts: • Area concepts require that children look at more than one measurable dimension • Capacity and volume have many everyday applications • Weight can be compared using balance scales or regular scales • Time is relative for young children and is best taught through everyday routines and conversations.

31. Basic Concepts of Measurement • Measurement varies with the size of the uit used to make the measurement • Accurate measurement depends on proper use of an appropriate tool • Estimation is useful in building basic concepts when things such as a million can be measured.

32. Basic Concepts in Data Key Concepts • The study of statistics involves collecting, organizing, and sorting data • Concepts of labeling and scaling are crucial to data representation • Data can be described through graphs, tables, and lists

33. Basic Concepts of Data Key Concepts: • The process of analyzing and interpreting data involves recognition of patterns or trends, and gaining information from graphs • In the process of organizing data, children make inferences or predictions, and have initial experiences with probability

34. Math Problem Solving Key Concepts: • Problem solving begins by sensing a problem and posing thoughtful questions • All the senses are used to collect information abut the problem to be solved • Information or data must be collected and organized in some representational way

35. Math Problem Solving Key Concepts: • Information collected-the data-is analyzed • The problem-solving processes are intimately involved in all areas of mathematics: knowledge of numbers, counting, measuring, graphing, beginning algebra, and geometry

36. Language and Writing in Math • Language and experiences go together • Demands listening, speaking, writing, and reading • Written language is necessary • Books are consulted and read • Math experiences must be continuous • Reflection is necessary • Rich environment • Vocabulary

37. Activity with Math Standards • What do you need to know? • Literature connection and needed resources • How to make home connections? • How to assess? • What will children need to do to demonstrate the concepts?

38. Websites of Interest www.sesamewhorkshop.org www.nickjr.com www.nctm.org (Illuminations) Pigseye.kennesaw.edu/~rouyang/ece4401/w-sites1.html www.center.edu (math their Way) www.carolhurst.com www.little-g.com/shockwave/frame.html www.ux1.eiu.edu/~cfsjy/mts/_link.htm www.learningpage.com/free_pages/menu_basics/numbers_zaner.html www.computerlab.kids.new.net/ www.storylineonline.com

39. SENSORY TUB MATHEMATICS • Not just for science

40. Introductions Math, Science, and Spanish PhD 4 year old Angela

41. Piaget • Knowledge constructed in the mind of the learner • Young Children think differently than older children and adults • Young children need a specialized instruction because of their concreteness and less logical thinking • Children learn from the environment, peers, and adults in school and beyond (culture acquiring)

42. Vygotsky • Added to Piaget’s theories • Moving children to higher levels is because of those interactions with more accomplished persons (older children and adults) • Guide by explaining, demonstrating, and questioning to reach higher cognitive thinking • Zone of Proximal development

43. Scientific Process • Formulate questions, collect data, and develop answers • Organize, reflect on, represent, and document investigations • Share and discuss ideas with others

44. Baby Test Tubes • This is not finished—what could it be if it continued down the assembly line?

45. Carol Seefeldt • The scientific inquiry process is observing, questioning, investigating, analyzing, and reaching conclusions and communicating the results to others • Give up “show and tell” in favor of group meetings

46. National Science Education Standards • Teachers should: • Plan inquiry based science programs • Guide and facilitate student learning • Engage in on-going assessment of teaching and learning • Develop environments that enable students to learn science

47. National Science Education Standards (Cont.) • Create learning communities of science learners • Equity • Provide a rich learning environment-you’re the facilitator • Model effective problem solving techniques • Have equipment for inquiry

48. Sciencing • Develop child’s innate curiosity about the world • Broaden procedural and thinking skills for investigating the world • Increase the child’s knowledge about the world • Emphasis on Inquiry

49. Themes in Science • Life science and the living environment • Earth science and the physical setting • Science in Personal and social perspective and the human organism • Physical Science, the physical setting and the designed world

50. Life science and the living environment • Key Concepts: • Plants require air, water, food, and light to live • There are many kinds of plants, and each has its own form or structure • Plants make seeds • Seeds grown into plants with roots, stems, leaves, and flowers • Plants grow and change