CURRICULUM EVALUATION

Citation and Skill Focus  Charles, R. I., et al. (1999). Math, Teacher’s Edition, Vol 2. New York: Scott Foresman-Addison Wesley. (Note: This is the second volume of the 1 st grade edition.)  Reading and writing numerals above 10

Strategy 1. Look in the table of contents and identify the likely lessons where the skill is being taught. 2. Look for a skills trace or scope and sequence that addresses where skills are taught for more information. 3. Limit or expand scope based on how many lessons you find.

Strategy cont. 4. Review lessons, focusing on issues addressed in Chapter 2 and on the instructional guidelines in the relevant chapter of the text. Strategies explicit and generalizable? Teaching procedures of high quality? (modeling, adequate examples, scaffolding) Sequence appropriate? Examples, practice and review adequate? Assessment aligned and frequent?

Table of Contents

Skills Trace First introduced IntroducedDevelopPractice/ Apply Review Make and write numbers to 19 Grade K , , 271 Count, add, and write groups of 10 Grade 1259 S60, , 271, , 420, 532 Write numbers to 60 as tens and extras Grade , , , 356, 420

Expand or Limit?  3-5 lessons…  Lessons 7-1, 7-2, 7-3.

Strategies?  Make and write numbers to 19  Use double ten frame. Give each student 19 counters.  “Have children count out 13 counters and place them on Workmat 3. How many ten frames did you fill? How many counters are left over? What number shows 10 and 3?”  Explicit?  Not bad. Strategy is replicable and steps are clear.  Generalizable?  Appropriate at conceptual stage. No focus on teaching reading and writing teen numbers without ten frame.

Strategies? Count and add groups of 10. Write the decade number. “For each number, ask children the following questions: How many counters are in each ten frame? How many ten frames are there? How many counters are there all together?” Explicit? Ok for teaching tens place value skill. Again, no model. Generalizable? Again, appropriate at conceptual stage, but not taken to the next level. They only say “Guide children to see that an easy way to add 20 and 10 would be to think: 2 tens and 1 ten is 3 tens, or thirty.”

Strategies?  Write numbers to 60 as tens and extras. “Explain that 2 groups of ten and 6 extras make 26. Help children verify by counting each object in the picture.” Then students have 3 more opportunities to count tens and extras to achieve a total. Explicit? Not very. (better would be…”first I count groups of tens, next…) Generalizable? Not very. Students are still learning in context of counting rather than focusing on place value and column alignment.

Teaching Procedures? For all skills Almost no modeling. Usually only one example. Teacher assistance is not gradually faded. It appears to go from high support to no support. Error correction is available, but not extensive. For example, in “Make and Write Numbers to 19” Observation: Children may have trouble counting out given numbers of counters. How to Help: Count aloud with the children as they touch or move the counters.

Sequencing General Guidelines  Preskills are taught before they are needed in strategies.  Easy skills are taught before more difficult ones.  Strategies and information that is likely to be confused are spaced or separated.

Sequencing  Make and write numbers to 19 (recommended from Stein text)  Preskills Reading: Read numerals between 0 and 10, rational counting of 2 groups. Writing: Read teen numbers accurately and fluently (i.e., 5 teen numbers at a rate of approximately 1 per sec.)  Sequence of instruction similar to reading teen numbers. Introduce first irregular teen about 2 days after regular teens; Then introduce at a rate of about 1 per day if students are successful.

Sequencing  Make and write numbers to 19 (from AW text)  Preskills taught:  Read and write numbers to 12  Addition  Sequence  All teens numbers introduced at once

 Sequencing  Count and add groups of 10. Write the decade number.  Preskill (recommended from Stein text): Count by 1s to 100; Skip count by 10s to 100  From AW text: Not clear where or if these preskills are addressed

Sequencing  Write numbers to 60 as tens and extras.  Preskill (recommended from Stein text): Read teens numbers accurately and fluently (5 teens numbers in 8 seconds); Count by 1s to 100; Skip count by 10s to 100; tens place value facts.  From AW text:  Teen numbers introduced, but not to fluency  Not clear whether Count bys and Skip counting were introduced.  Tens place value facts in previous lesson, but not to mastery.

Practice and Review  Initially massed to solidify students knowledge  Opportunity to practice discriminating between similar skills or concepts.  Distributed  Revisited over time  Accumulated  Concepts that are initially taught separately are reviewed together  Varied  Concepts are applied to a range of applications to promote generalization

Practice and Review First introduced IntroducedDevelopPractice/ Apply Review Make and write numbers to 19 Grade K , , 271 Count, add, and write groups of 10 Grade 1259 S60, , 271, , 420, 532 Write numbers to 60 as tens and extras Grade , , , 356, 420

Practice and Review  Make and write numbers to 19  9 practice pages total 16 items for introduction Practice page: 8 items Reteaching page: 4 items Enrichment page: 2 items Problem Solving page: 5 items Practice Game: unlimited Stop and Practice: 7 items Mixed practice: 4 items

Practice and Review  Count and add groups of ten  13 pages total Introduction: 15 items Practice page: 11 items Reteaching page: 8 items Enrichment page: 7 items Problem Solving page: 5 items Mixed Practice: 1 item Cumulative Review: 1 item Skill Practice Bank: 6 items

Assessment and Instruction Link  Placement tests?  No  Recommendations for acceleration and remediation?  Yes, but limited “Another way to learn” section “Options for reaching all learners” Enrichment and problem solving pages Reteaching page  Assessments carefully aligned with instruction?  Not really. Assessment in “Close and Assess” section

Conclusions  Strategies are reasonably explicit, but not highly generalizable  Teaching procedures are not well-articulated, although there are some error correction procedures  Sequencing is weak. Preskills possibly taught, but not to mastery. New skills not sequenced well.  Practice and review needs work. Perhaps adequate initial practice, but not for discriminative, distributed, and varied.  Assessment needs to be more frequent and aligned.

Adaptations for Students in Special Education  Add more modeling of strategies  Provide more scaffolding (leading) on how to apply strategies  Assess preskills and make sure they are firmly taught.  Improve sequence of instruction. For example, introduce regular teens first, then irregular.  Add additional practice and review. Focus on appropriate discriminative practice. Distribute over time.  Plan for more frequent assessment opportunities. Align to instruction more closely.