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Literature review","","This appendix reviews research and evidence on how students’ foundational knowledge and skills in grade 7 relate to Missouri students’ Algebra I achievement in grade 8. It examines why Algebra I in grade 8 can expand access to advanced pathways while also posing risks when students skip other grade 8 math content. The review synthesizes findings on algebraic thinking components—generalizing, representing/justifying generalizations, and reasoning—alongside discussion of instructional readiness and the use of state assessment domain scores to identify students ready for Algebra I.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/what-grade-7-foundational-knowledge-and-skills-are-associated-with-missouri-students-algebra-i-achievement-in-grade-8-appendix-a-literature-review/587490/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/what-grade-7-foundational-knowledge-and-skills-are-associated-with-missouri-students-algebra-i-achievement-in-grade-8-appendix-a-literature-review/587490.png","ImageObject",300,407,{"name":92,"@type":93},"นรินทร์","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why do some districts enroll middle school students in Algebra I?","Question",{"text":112,"@type":113},"Success in advanced math courses expands students’ access to more college and career options. Many districts enroll students in Algebra I because it acts as a gateway course to further advanced study.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What foundational skills are emphasized as part of algebraic thinking?",{"text":117,"@type":113},"Research cited in the appendix identifies three components: generalizing math ideas; representing and justifying generalizations in multiple ways; and reasoning with generalizations.",{"name":119,"@type":110,"acceptedAnswer":120},"How can educators identify which students are ready to take Algebra I in grade 8?",{"text":121,"@type":113},"The appendix discusses using state assessment data, including domain scores from statewide tests such as the Missouri Assessment Program, as a feasible alternative to administering additional readiness tests.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},587490,1792230260,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},2336475104957,"https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136","APPENDIXES July 2020  \nRegional Educational Laboratory Central  \nAt Marzano Research  \nWhat Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students’ Algebra I Achievement in Grade 8?  \nAppendix A. Literature review  \nAppendix B. Methods  \nAppendix C. Supporting analysis  \nAppendix D. Other analyses using proficiency groups as the dependent variable See  [https://go.usa.gov/xwuzB](https://go.usa.gov/xwuzB for)[ for](https://go.usa.gov/xwuzB for) the full report.  \nAppendix A. Literature review  \nSuccess in advanced math courses provides students access to a wider variety of college and career options (National Mathematics Advisory Panel, 2008) . To increase opportunities for students to take more advanced math courses in high school, many school districts enroll middle school students in Algebra I, a gateway course for advanced math (Star et al., 2015) . Between 1990 and 2011, the proportion of students taking Algebra I or more advanced math courses in middle school doubled (Domina, 2014) .  \nBut students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational knowledge and skills required for success in advanced math courses (Domina, McEachin, Penner, & Penner, 2015) . Math is a sequential and cumulative discipline (Pillay, Wilss, & Boulton-Lewis, 1998): learning builds as students progress from grade to grade. Students typically begin with number concepts and skills and then move to more abstract ideas, such as working with generalized quantities (for example, functional relationships like y = 2 + 3x, in which variables do not represent one specific value) . Therepetition of concepts and skills that was common across grades in the past meant that only about 30 percent of the content in grade 8 textbooks was new (Flanders, 1987) . Thus, students could be accelerated with little concern about what content they would skip or how their understanding of content would be advanced.  \nHowever, current standards are more developmental and linear in that they exhibit less overlap in content from grade to grade. Additionally, the content of standards has shifted considerably with regard to development of algebraic concepts and skills before students enter high school. For example, the Common Core State Standards Initiative (2011) includes a domain focused on operations and algebraic thinking that begins in kindergarten and progresses through grade 5. That domain leads directly into the domain of expressions and equations, which is a focus from grade 6 onward. In the expressions and equations domain, solving systems of linear equations is now a standard for all grade 8 students (Common Core State Standards Initiative, 2011) . Students who skip grade 8 general math to take Algebra I might miss opportunities to develop an understanding of the process for solving systems of equations and other topics emphasized at that grade level. Therefore, educators face the challenge of determining which students can successfully skip grade 8 math to take Algebra I and which students will benefit from taking grade 8 math before Algebra I.  \nREL 2020–023 A-1  \nFactors that influence student readiness for Algebra I in grade 8  \nA large body of research has examined the types of experiences that students need in order to be successful in Algebra I (for example, Blanton, 2008; Blanton, Levi, Crites, Dougherty, & Zbiek, 2011; Carpenter, Levi, Berman, & Pligge, 2005; Carraher, Martinez, & Schliemann, 2008; Dougherty, 2008; Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015) . That research has identified three components that form the basis of algebraic thinking that should be incorporated into approaches to introducing content before Algebra I: generalizing math ideas; representing and justifying generalizations in multiple ways (natural language, tables, charts, graphs, symbols, and physical materials); and reasoning with generalizations (Bla","cbCairSBesbyNIB0","https://ap.wps.com/l/cbCairSBesbyNIB0","pdf",1225212,22,"English","# Appendix A. Literature review\n## Algebra I access versus missed foundational skills\n## Standards progression and domain alignment\n## Factors forming algebraic thinking\n## Using state assessment data for readiness\n## Focus on Missouri Assessment Program domains","[{\"question\":\"Why do some districts enroll middle school students in Algebra I?\",\"answer\":\"Success in advanced math courses expands students’ access to more college and career options. Many districts enroll students in Algebra I because it acts as a gateway course to further advanced study.\"},{\"question\":\"What foundational skills are emphasized as part of algebraic thinking?\",\"answer\":\"Research cited in the appendix identifies three components: generalizing math ideas; representing and justifying generalizations in multiple ways; and reasoning with generalizations.\"},{\"question\":\"How can educators identify which students are ready to take Algebra I in grade 8?\",\"answer\":\"The appendix discusses using state assessment data, including domain scores from statewide tests such as the Missouri Assessment Program, as a feasible alternative to administering additional readiness tests.\"}]","What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students’ Algebra I Achievement in Grade 8? - Appendix A. Literature review | PDF",1792061987,55]