Week One Thoughts

What does the term early childhood mathematics mean to you?

Early Childhood Mathematics means that children are learning basic and practical math and thinking skills that will prepare them for more complex and real life math skills in the future. Children must have a very concrete knowledge of basic mathematics before trying to understand more abstract math.

What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?

• children construct their own knowledge
• connect any new information to information students already know
• children can learn from their peers when they share their ideas
• manipulatives are very important
• math should be challenging and taught through problem-solving
• math should be student-centered rather than teacher-centered
• students need to do more than solve the problem, they should explain how they got the answer
• give hints instead of answering problems for students, help them work through it rather than giving them an answer

Challenge Four

Jim: "Because I added, 3 with 7, that makes ten, then added 3 more, and that's 13", "grouped it down-(counting down)", "flipped them over (counting down again)", 13 take away 3 would be 10 and 10 take away 1 is 9

Lauren: 7+7=14, so 7+6=13, counts down in groups of numbers

Elizabeth: 7+7=14, so 7+6=13, knows six is one less than 7, so that makes the answer 13 instead of 14, grouping-5+5=10, 10+2=12

Derek: [video wouldn't load properly]

Students have learned to add and subtract by grouping. Students have also had more practice with adding and subtracting larger numbers. Students know how to subtract by counting down. Students have a better concepts of number relationships. Students rely less on using fingers or objects to add and subtract and focus more on doing the math mentally and reasoning out the problems.

Challenge Three

Jim: subtraction, mental math, 7+6=9, 8+5="they didn't teach me that", 12 cows in barn-4 came outside. how many are left? "11 are left, just thought about it for just a minute", 4 cows in barn, 1 came outside 3 are left, 3 comes before 4

Lauren: counting up from the smallest number to add, uses dots & patterns to add, "i counted in my mind", counted backwards from 12

Elizabeth: guessed, memorization, counted cows, added 4+2 by counting up to 6

Derek: counted up to 7 starting with 5, did not know how to subtract, but he could add

Most of the students could match objects with numbers. They knew how to count objects and that numbers could represent the objects. Students also knew how to count. One of the students had memorized several of the answers to the problem which probably means she has had a lot of practice doing the problems. The students could add by using mental math or using their fingers to count. A couple of the students knew how to subtract. Sometimes the students had trouble explaining how they got an answer or why they didn't know how to solve one of the math problems.

As a teacher I would first make sure the students had a basic understanding of numbers, counting, adding, and subtracting. I would have the children to do math drills to make it easier for them to have most of the simple problems memorized so that they would not have to count of their fingers or spend much time trying to find an answer for the problem. Then, I would focus on teaching the students how to explain how they arrived at an answer.

Challenge Two

What instructional activities would you use to enhance student learning?

• use manipulatives (blocks, counting bears, etc.)
• hands-on experiences in groups
• have specific centers set up around the classroom
• allow students to work in pairs and challenge each other to add, subtract and group manipulatives in different ways
• integrate math into other subjects
• integrate prior knowledge to more challenging ideas
• use real life situations

Challenge One

What can first grade students do related to math?

• add, subtract
• recognize numbers and their symbols
• number sequence
• count
• skip count
• identify numbers that are greater than or less than others
• identify simple number patterns
• identify even and odd numbers