AlibaliM. W.KnuthE. J.HattikudurS.McNeilN. M.StephensA. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221–247. doi:10.1080/10986060701360902
2.
BlantonM.LeviL.CritesT.DoughertyB. (2011). Developing essential understanding of algebraic thinking Grades 3–5. Reston, VA: National Council of Teachers of Mathematics.
3.
BobisJ.ClarkeB.ClarkeD.ThomasG.WrightB.Young-LoveridgeJ.GouldP. (2005). Supporting teachers in the development of young children’s mathematical thinking: Three large scale cases. Mathematics Education Research Journal, 16, 27–57. doi:10.1007/BF03217400
4.
ByrdC. E.McNeilN. M.ChesneyD. L.MatthewsP. G. (2015). A specific misconception of the equal sign acts as a barrier to children’s learning of early algebra. Learning and Individual Differences, 38, 61–67. doi:10.1016/j.lindif.2015.01.001
5.
CosseyR.KostelnikL.RandelM.ScottM.ZolliL. (2012). Math reasoning inventory. New York, NY: Scholastic.
6.
Council of Chief State School Officers & National Governors Association Center for Best Practices. (2010). Common Core State Standards for mathematics. Washington, DC: Author. Retrieved from http://corestandards.org
7.
FalknerK. P.LeviL.CarpenterT. P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232–236.
8.
FloresM. M.HintonV. M.SchweckK. B. (2014). Teaching multiplication with regrouping to students with learning disabilities. Learning Disabilities Research & Practice, 29, 171–183. doi:10.1111/ldrp.12043
9.
GerstenR.BeckmannS.ClarkeB.FoegenA.MarshL.StarJ. R.WitzelB. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: Institute of Education Sciences.
10.
GrahamK.CuocoA.ZimmermannG. (2010). Focus in high school mathematics: Reasoning and sense making in algebra. Reston, VA: National Council of Teachers of Mathematics.
11.
HattikudurS.AlibaliM. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help?Journal of Experimental Child Psychology, 107, 15–30. doi:10.1016/j.jecp.2010.03.004
12.
HengM. A.SudarshanA. (2013). “Bigger number means you plus!” Teachers learning to use clinical interview to understand students’ mathematical thinking. Educational Studies in Mathematics, 83, 471–485. doi:10.1007/s10649-013-9469-3
13.
HeritageM. (2013). Formative assessment in practice: A process of inquiry and action. Cambridge, MA: Harvard Education Press.
14.
HodgesT. E.RoseT. D.HicksA. D. (2012). Interviews as RtI tools. Teaching Children Mathematics, 19, 30–36. doi:10.5951/teacchilmath.19.1.0030
15.
HuntJ. H.EmpsonS. B. (2015). Exploratory study of informal strategies for equal sharing problems of students with learning disabilities. Learning Disability Quarterly, 38, 208–220. doi:10.1177/0731948714551418
16.
KnuthE. J.StephensA. C.McNeilN. M.AlibaliM. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37, 297–312.
17.
McNeilN. M.AlibaliM. W. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6, 285–306. doi:10.1207/s15327647jcd0602_6
18.
National Center for Education Statistics. (2015a). NAEP data explorer, 2015 mathematics assessment. Washington, DC: Institute of Education Sciences, U.S. Department of Education. Retrieved from http://nces.ed.gov/nationsreportcard/about/naeptools.asp
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
21.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.
22.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
23.
Newman-GoncharR.ClarkeB.GerstenR. (2009). A summary of nine key studies: Multi-tier intervention and response to interventions for students struggling in mathematics. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
24.
PowellS. R. (2012). Equations and the equal sign in elementary mathematics textbooks. Elementary School Journal, 112, 627–648. doi:10.1086/665009
25.
PowellS. R. (2015). The influence of symbols and equations on understanding mathematical equivalence. Intervention in School and Clinic, 50, 266–272. doi:10.1177/1053451214560891
26.
PowellS. R.DriverM. K.JulianT. E. (2015). The effect of tutoring with nonstandard equations for students with mathematics difficulty. Journal of Learning Disabilities, 48, 523–534. doi:10.1177/0022219413512613
27.
ShermanJ.BisanzJ. (2009). Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives. Journal of Educational Psychology, 101, 88–100. doi:10.1037/a0013156
28.
StephensA. C.KnuthE. J.BlantonM. L.IslerI.GardinerA. M.MarumT. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32, 173–182. doi:10.1016/j.jmathb.2013.02.001
29.
TobeyC. R.MintonL. G. (2010). Uncovering student thinking in mathematics, Grades K–5: 25 formative assessment probes for the elementary classroom. Thousand Oaks, CA: Corwin.
30.
UsiskinZ. (1995). Why is algebra important to learn?American Educator, 19, 30–37.
31.
WitzelB. S.MercerC. D.MillerM. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121–131. 10.1111/1540-5826.00068