Math for Pre-Kindergarten T/TAC at VCU
Your concerns Students have difficulty with: • Recognizing the numerals 1-10 • Counting • One-to-one correspondence • Half and whole • Patterns • Writing the numbers 1-10
Let’s examine… • Assessment • Curriculum • Instruction
You may see… Four year olds: - spontaneously use math to solve real problems - begin to develop one-to-one correspondence with small groups - estimate quantities randomly - sort objects by classifying
Five year olds: - count objects up to 10 with few mistakes - recognize more complex patterns - enjoy beginning games that involve moving markers around a board - use relationship words
- solve multi-piece puzzles - sequence 5 or more objects - classify objects into sets - count a small number of objects and recall that number - confuse sets within sets (Stupiansky and Stupiansky, 1992)
To make the best instructional decisions for children, teachers need to assess each child’s pattern of development, knowledge, attitudes, and interests. (Copley, 2000)
What is assessment? It’s the process of observing, gathering evidence about a child’s knowledge, behaviors, and dispositions; documenting the work that children do and how they do it; and making inferences from that evidence for a variety of purposes. (Copley 2000)
Benefiting children - takes place before, during, and after instruction - make adjustments to curriculum and instruction - identify the strengths and needs of children Observing and Listening - observe children’s actions, behavior, and interactions with others - develop good questioning skills - use the information to plan instruction
Use Multiple Sources of Evidence - samples of children’s work - anecdotal records - audiotaped descriptions of problem solving discussions Assessing learning and development - teachers assessing their own growth - assessing children’s growth in math understanding (Copley, 2000)
We should not rely on a single whole group assessment to measure student’s mathematical competence. • Teachers must try not to allow assessment to narrow curriculum and inappropriately label children. • The assessment process should help build mathematical competence and confidence. It should be continuous, well-implemented, and well-conceived. (NAEYC, 2002)
Activity • With a partner • Read the enclosed scenario • Highlight the different principles of assessment • Think of a time in your classroom when you have had a similar assessment experience with your whole group
In your classroom • What are the different ways you assess and document your children’s knowledge of concepts? • At what times and during what activities do you assess and document?
Documentation of Students’ Progress • Portfolios • Individual and group products • Observations • Child self-reflections • Narratives of learning experiences (Helm & Gronlund, 2000)
Activity Read about Rachel and Tiffany. • What do you know about Rachel? • What do you know about Tiffany?
NCTM Recommendations for Mathematics Education for 3-6 Year Olds • Enhance children’s interest in mathematics and their dispositions to use it to make sense of their physical and social worlds • Build on children’s experience and knowledge, including their family, linguistic, cultural, and community backgrounds; their individual approaches to learning; and their informal knowledge
Base mathematics curriculum and teaching practices on knowledge of young children’s cognitive, linguistic, physical, and social-emotional development • Use curriculum and teaching practices that strengthen children’s problem-solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas
Ensure that the curriculum is coherent and compatible with known relationships and sequences of important mathematical ideas • Provide for children’s deep and sustained interaction with key mathematical ideas • Integrate mathematics with other activities and other activities with mathematics • Provide ample time, materials, and teacher support for children to engage in play
Actively introduce mathematical concepts, methods, and language through a range of appropriate experiences and teaching strategies • Support children’s learning by thoughtfully and continually assessing all children’s mathematical knowledge, skills, and strategies
Implications for your classroom • Examine your curriculum. • Whole group or individual instruction? • Plan the environment and activities to meet the needs of the student(s). • Interact with the student(s) and assist with the development of mathematical language.
Examine your curriculum • Are you integrating, i.e. thematic units or the Project Approach, so the skill can be in many areas of the curriculum? • Have I specifically focused on this concept/skill in my interactions with the students? • Do I need to revisit this concept/skill with the class? • Is it a developmentally appropriate time to be doing this concept/skill?
Whole Group or Individual Instruction • Who has not mastered this concept/skill? • Do I need to work with all of the children, some of the children, or one child?
Plan the Environment and Activities • Do I have a math rich environment? • Do I have manipulatives available to the children? • Does my schedule provide time for the students to interact with others and to apply the concepts/skills? • Are the experiences meaningful, active, naturalistic, and developmentally appropriate?
Interactions with Students • Plan experiences when you can guide a student’s understanding of a concept through your use of specific vocabulary and questioning techniques.
Activity How would you assist Rachel with her mathematical understanding of one-to-one correspondence and seriation?
A Plan for Planning It assists you with making decisions for your students. 1. How will they demonstrate the concept or skill in the classroom? 2. How can you set up my environment? 3. What learning experiences will we have?
One-to-one correspondence and counting SOL K.1: “The student, given a set containing 10 or fewer concrete items, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.”
One-to-one correspondence and counting SOL K.2: “The student, given a set containing 10 or fewer concrete items, will a) tell how many are in the set by counting the number of items orally; b) select the corresponding numeral from a given set; and c) write the numeral to tell how many are in the set.”
One-to-one correspondence and counting • Children often recite numbers as they touch items to count them without the awareness that each item corresponds with one word in the counting sequence. • Children need to construct the mental structure of number and to assimilate the words into this structure. (Kamii, 1982)
One-to-one correspondence and counting Proportion of children who counted nine objects correctly (Meljac, 1979):
Developmental progression through these abilities: 1. The ability to say the words in the correct sequence. 2. The ability to count objects (i.e. make a one-to-one correspondence between the words and the objects). 3. The choice of counting is the most desirable tool. (Kamii, 1982)
Implications for the classroom • Ask children to make sets, instead of make a judgment about sets • Provide opportunities to explore with number concepts • Encourage children to exchange ideas with each other • Observe the child’s behavior to ascertain what he/she is thinking (Kamii, 1982)
Patterns and Classification SOL K.17: “The student will sort and classify objects according to similar attributes (size, shape, and color).” SOL K.18: “The student will identify, describe, and extend a repeating relationship (pattern) found in common objects, sounds, and movements.”
Patterns and Classification • Identify the stage of development for the child. • Most young children can classify objects. It’s the vocabulary that they may be missing. The lack of vocabulary may be mistaken for lack of knowledge or ability to classify. (Kriova & Bhargava, 2002) • Exploring attributes, sorting, matching, working with differences and gradual variations, and creating patterns and order assist young children to organize and make sense of their world. (Hohmann & Weikhart, 2002)
Implications for the classroom • Opportunities will arise through play to support the development of these concepts. • Have a variety of materials available to students. • Provide many different learning experiences for large group, small group, and individual learning.
In summary… • Assessment is the first step. • Curriculum and instruction decisions are made from on-going assessments. • It’s a continuous process.
Additional Resources • Websites • NCTM standards for PreK-2 • SOL Curriculum Framework • Literature • Software
For additional information please visit our website at: http://www.vcu.edu/ttac or participate in our online community at http://ttacoline.org