CURRICULUM EVALUATION

Citation and Skill FocusCharles, R. I., et al. (1999). Math, Teachers Edition, Vol 2. New York: Scott Foresman-Addison Wesley. (Note: This is the second volume of the 1st grade edition.)

Reading and writing numerals above 10

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

Strategy cont. 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 introducedIntroducedDevelopPractice/ ApplyReviewMake and write numbers to 19Grade K257257258, 263-274, 271Count, add, and write groups of 10Grade 1259259S60, 263-264, 271, 532356, 420, 532Write numbers to 60 as tens and extrasGrade1261261262, 263-264, 271346, 356, 420

Expand or Limit?3-5 lessonsLessons 7-1, 7-2, 7-3.

Strategies?Make and write numbers to 19Use 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 befirst 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 skillsAlmost 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 19Observation: 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.

SequencingGeneral GuidelinesPreskills 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.

SequencingMake 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.

SequencingMake and write numbers to 19 (from AW text)Preskills taught:Read and write numbers to 12AdditionSequenceAll teens numbers introduced at once

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

SequencingWrite 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 fluencyNot clear whether Count bys and Skip counting were introduced. Tens place value facts in previous lesson, but not to mastery.

Practice and ReviewInitially massed to solidify students knowledgeOpportunity to practice discriminating between similar skills or concepts. DistributedRevisited over timeAccumulatedConcepts that are initially taught separately are reviewed togetherVariedConcepts are applied to a range of applications to promote generalization

Practice and Review

First introducedIntroducedDevelopPractice/ ApplyReviewMake and write numbers to 19Grade K257257258, 263-274, 271Count, add, and write groups of 10Grade 1259259S60, 263-264, 271, 532356, 420, 532Write numbers to 60 as tens and extrasGrade1261261262, 263-264, 271346, 356, 420

Practice and ReviewMake and write numbers to 199 practice pages total16 items for introductionPractice page: 8 itemsReteaching page: 4 itemsEnrichment page: 2 itemsProblem Solving page: 5 itemsPractice Game: unlimitedStop and Practice: 7 itemsMixed practice: 4 items

Practice and ReviewCount and add groups of ten13 pages totalIntroduction: 15 itemsPractice page: 11 itemsReteaching page: 8 itemsEnrichment page: 7 itemsProblem Solving page: 5 itemsMixed Practice: 1 itemCumulative Review: 1 itemCumulative Review: 1 itemSkill Practice Bank: 6 items

Assessment and Instruction LinkPlacement tests?NoRecommendations for acceleration and remediation?Yes, but limitedAnother way to learn sectionOptions for reaching all learnersEnrichment and problem solving pagesReteaching pageAssessments carefully aligned with instruction?Not really.Assessment in Close and Assess section

ConclusionsStrategies are reasonably explicit, but not highly generalizableTeaching procedures are not well-articulated, although there are some error correction proceduresSequencing 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 EducationAdd more modeling of strategiesProvide more scaffolding (leading) on how to apply strategiesAssess 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.

*More steps in strategy the more difficultexample: addition problems that require regrouping (carrying) are more difficult than those that do not.Prior to being introduced to carrying students need to be firm on 1) adding without carrying and 2) place value

Separating likely to confuse information: 6 and 9 identification (b and d)Sufficient initial examples? Not reallyDiscrimination practice? Noonly Mixed practiceCumulative review? no*Sufficient initial examples? Not reallyDiscrimination practice? Yes, in Mixed practice, cumulative review and skill practice, but limited items. Cumulative review? Yes, but spread across the text and limited.

*