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Learn how math instruction has evolved from computation to application through critical thinking skills. Discover strategies and resources to help your second grader understand and excel in math.
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Past and Present… • In the past, Math instruction focused on computation. • Now, Math instruction focuses on APPLICATION through the use of critical thinking skills, higher order thinking and depth of knowledge in order to solve/analyze multi-step problems.
At school… Mathematics Teaching Practices: 1 – Establish Mathematics Goals to Focus on Learning. 2 – Implement Tasks that promote reasoning and problem solving. 3 – Use and connect mathematical representations. 4 – Facilitate meaningful mathematical discourse. 5 – Pose purposeful questions. 6 – Build procedural fluency from conceptual understanding. 7 – Support productive struggle in learning mathematics. 8 – Elicit and use evidence of student thinking.
During instruction students … • Use the textbook • Use manipulatives and math tools • Use their Math Journals to explore/write about: “Essential Question, Problem of the Day, justify their work/answers • Use task cards, anchor sheets • Participate in “Math Talks” and cooperative learning groups • Math drills • Computer programs for enrichment/remediation • Whole Group/Small group/Independent instruction
Three types of Mathematical understanding- CPR • Conceptual -- What do students need to know? • Procedural -- What do students need to do? • Representational -- What do students need to show?
How can we get our students to UNDERSTAND math? • Students can understand Math by: building FLUENCY and using STRATEGIES.
3 Elements of Fluency • Accuracy (Correctness) • Efficiency (Quick retrieval of facts both written and oral.) • Flexibility (Use of strategies to help with recall.) • Reading/Writing capability also play a major role.
Prerequisites • Before children can conceptually understand addition and subtraction facts they must first have one-to-one correspondence, conservation of numbers, and they must know the counting sequence.
Counting Sequence • Knowing the counting sequence is as simple as knowing what number comes next. Just because a child knows the counting sequence does not mean that they understand numbers, but it is an important step in the development of numbers.
One-to-one Correspondence • Understanding that one item is represented by a unique count.
Conservation of Number • The final item counted tells the number in the group. Seven items are counted so there are seven items in the group.
Why learn strategies? • Students can develop fluency with their addition and subtraction facts if they memorize strategies such as: the Doubles facts & the Tens facts. The rest of the facts can be derived using strategies. • Efficient use of strategies leads to a better understanding of numbers, and the properties of addition. • Better conceptual understanding promotes long lasting procedural understanding and ultimately results in quick retrieval of all facts. That is the goal. Quick retrieval of all facts.
Strategies that promote understanding…
How does it work? • 6 + 6 = 12 so, • 6 + 7 = 13 because • 6 + 6 + 1 = 12 + 1 = 13 Or • 7 + 7 = 14 so, • 6 + 7 = 13 because • (7 - 1) + 7 = 14 – 1 = 13
Add tens and ones Adding tens and ones places an emphasis on place value and expanded form.
How does it work? 8 + 6 = 14 Use a visual model to promote “Cardinality”. Cardinality is recognizing a number by the configuration – no counting needed. 8 + (2 + 4) = 14 Decompose 6 into 2 and 4 (8 + 2) + 4 = 14 Use the Associative Property to make a ten with 8 and 2 10 + 4 = 14 Now the number is in expanded form and place value makes it easy to add.
Subtraction • Think addition when solving subtraction problems. Fact families and related math facts. • 9 – 5 = 4 because • 5 + 4 = 9
Equal Groups • Sarah has three pages of stickers. There are four stickers on each page. How many stickers are there?
Array Model • Max made three rows of tiles. He put four tiles in each row. How many tiles are there?
What to Do When Teaching Basic Facts • Develop conceptual understanding using strategies • Ask students to self-monitor • Focus on self-improvement • Drill in short time segments • Work on facts over time • Involve families • Make practice/drill enjoyable • Use technology • Emphasize the importance of quick recall of facts
More “to Do-s”… • Practice makes BETTER! • Use manipulatives, anchor sheets, & task cards. • SHOW YOUR WORK! • Explain your answer. Know the “WHY”
What Not to Do When Teaching Basic Facts • Don’t use lengthy drilling • Don’t proceed through the facts in order from 0 to 9 • Don’t move to memorization too soon • Don’t use facts as a barrier to good mathematics
Remediation • Focus on reasoning strategies • Recognize that more drill will not work • Provide hope • Inventory the known and unknown facts • Diagnose strengths and weaknesses • Build in success • Provide engaging activities
TESTING • Second Grade- SAT • Third Grade-FSA
SAT- The Math portion of the SAT is auditory. Questions are read aloud to students.
Looking ahead to Third Grade… • Upon entering third grade, your child should have show mastered: • Adding/subtracting with regrouping • Telling time • Counting money • Estimating 10-100 • Math operations Start practicing multiplication BEFORE the third grade school year; during the summer. Promote good study habits.
Third Grade FOCUS Here are some strategies that will help your child get ready for third grade.
Multiply by 2: Doubling 2 x 8 = 8 + 8 = 16
Division • Think multiplication when solving division problems. • 24 ÷ 6 = • 6 x __ = 24
