Dimensions of Learning Probability Vocabulary

Normative discourse about probability requires shared meanings for disciplinary vocabulary. Previous research indicates that students’ meanings for probability vocabulary often differ from those of mathematicians, creating a need to attend to developing students’ use of language. Current standards documents conflict in their recommendations about how this should occur. In the present study, we conducted microgenetic research to examine the vocabulary use of four students before, during, and after lessons from a cycle of design-based research attending to probability vocabulary. In characterizing students’ normative and nonnormative uses of language, we draw implications for the design of curriculum, standards, and further research. Specifically, we illustrate the importance of attending to incrementality, multidimensionality, polysemy, interrelatedness, and heterogeneity to foster students’ probability vocabulary development.

Footnotes

This material is based on work supported by the National Science Foundation Grant DRL-1356001. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Journal for Research in Mathematics Education
  • 1.

    Australian Curriculum Assessment and Reporting Authority. (2015). Mathematics – Sequence of content. Retrieved from http://www.acara.edu.au/verve/_resources/Mathematics_-_Sequence_of_content.pdf

    • Search Google Scholar
    • Export Citation
  • 2.

    BakkerA & van EerdeD (2015). An introduction to design-based research with an example from statistics education. In Bikner-AhsbahsAKnippingC & PresmegN (Eds.) Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 429466). Dordrecht, the Netherlands: Springer. doi:https://doi.org/10.1007/978-94-017-9181-6_16

    • Search Google Scholar
    • Export Citation
  • 3.

    CaiJMorrisAHohenseeCHwangSRobisonV & HiebertJ (2017). A future vision of mathematics education research: Blurring the boundaries of research and practice to address teachers’ problems. Journal for Research in Mathematics Education48(5) 466473. doi:https://doi.org/10.5951/jresematheduc.48.5.0466

    • Search Google Scholar
    • Export Citation
  • 4.

    Certain. (n.d.). In Lexico: Powered by Oxford. Retrieved from https://www.lexico.com/en/definition/certain

  • 5.

    ChinnCA & SherinBL (2014). Microgenetic methods. In SawyerRK (Ed.) The Cambridge handbook of the learning sciences (2nd ed. pp. 171190). New York, NY: Cambridge University Press. doi:https://doi.org/10.1017/cbo9781139519526.012

    • Search Google Scholar
    • Export Citation
  • 6.

    ConfreyJMaloneyAPNguyenKLeeKSPanorkouNCorleyD & GibsonT (2012). TurnOnCCMath.net: Learning trajectories for the K-8 Common Core State Math Standards. Retrieved from https://www.turnonccmath.net

  • 7.

    The Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher32(1) 58. doi:https://doi.org/10.3102/0013189X032001005

    • Search Google Scholar
    • Export Citation
  • 8.

    Encyclopaedia Britannica. (2003). Mathematics in context: Take a chance. Chicago, IL: Britannica.

  • 9.

    FischbeinENelloMS & MarinoMS (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics22(6) 523549. doi:https://doi.org/10.1007/BF00312714

    • Search Google Scholar
    • Export Citation
  • 10.

    FrankeMLWebbNMChanAGIngMFreundD & BatteyD (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education60(4) 380392. doi:https://doi.org/10.1177/0022487109339906

    • Search Google Scholar
    • Export Citation
  • 11.

    GildeaPMMillerGA & WurtenbergCL (1990). Contextual enrichment by videodisc. In NixD & SpiroR (Eds.) Cognition education and multimedia: Exploring ideas in high technology (pp. 129). Hillsdale, NJ: Lawrence Erlbaum Associates.

    • Search Google Scholar
    • Export Citation
  • 12.

    GlesneC (2016). Becoming qualitative researchers: An introduction (5th ed.). Boston, MA: Pearson.

  • 13.

    GreenDR (1983). A survey of probability concepts in 3000 pupils aged 11-16 years. In GreyDRHolmesPBarnettV & ConstableGM (Eds.) Proceedings of the first International Conference on Teaching Statistics (pp. 766783). Sheffield, UK: Organising Committee of the First International Conference on Teaching Statistics.

    • Search Google Scholar
    • Export Citation
  • 14.

    GreerB & MukhopadhyayS (2005). Teaching and learning the mathematization of uncertainty: Historical, cultural, social and political contexts. In JonesGA (Ed.) Exploring probability in school (pp. 297324). New York, NY: Springer. doi:https://doi.org/10.1007/0-387-24530-8_13

    • Search Google Scholar
    • Export Citation
  • 15.

    GrothREBergnerJABurgessCRAustinJW & HoldaiV (2016). Re-imagining education of mathematics teachers through undergraduate research. Council on Undergraduate Research Quarterly36(3) 4146. doi:https://doi.org/10.18833/curq/36/3/6

    • Search Google Scholar
    • Export Citation
  • 16.

    GrothREButlerJ & NelsonD (2016). Overcoming challenges in learning probability vocabulary. Teaching Statistics38(3) 102107. doi:https://doi.org/10.1111/test.12109

    • Search Google Scholar
    • Export Citation
  • 17.

    HallidayMAK (1978). Language as social semiotic: The social interpretation of language and meaning. Baltimore, MD: University Park Press.

    • Search Google Scholar
    • Export Citation
  • 18.

    HiebertJ & LefevreP (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In HiebertJ (Ed.) Conceptual and procedural knowledge: The case of mathematics (pp. 128). Hillsdale, NJ: Erlbaum. doi:https://doi.org/10.4324/9780203063538

    • Search Google Scholar
    • Export Citation
  • 19.

    HofferWW (2016). Developing literate mathematicians: A guide for integrating language and literacy instruction into secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 20.

    HuntingRP & DavisGE (1991). Dimensions of young children’s conceptions of the fraction one half. In HuntingRP & DavisG (Eds.) Early fraction learning (pp. 2753). New York, NY: Springer. doi:https://doi.org/10.1007/978-1-4612-3194-3

    • Search Google Scholar
    • Export Citation
  • 21.

    Impossible. (n.d.). In Merriam Webster’s online dictionary. Retrieved from http://www.merriam-webster.com/dictionary/impossible

  • 22.

    JonesGALangrallCW & MooneyES (2007). Research in probability: Responding to classroom realities. In LesterFKJr (Ed.) Second handbook of research on mathematics teaching and learning (pp. 909955). Charlotte, NC: Information Age.

    • Search Google Scholar
    • Export Citation
  • 23.

    JonesGAThorntonCALangrallCW & TarrJE (1999). Understanding students’ probabilistic reasoning. In StiffLV & CurcioFR (Eds.) Developing mathematical reasoning in Grades K-12: 1999 Yearbook of the National Council of Teachers of Mathematics (pp. 146155). Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 24.

    KaplanJJFisherDG & RognessNT (2009). Lexical ambiguity in statistics: What do students know about the words association, average, confidence, random and spread? Journal of Statistics Education17(3) 119. doi:https://doi.org/10.1080/10691898.2009.11889535

    • Search Google Scholar
    • Export Citation
  • 25.

    KonoldC (1989). Informal conceptions of probability. Cognition and Instruction6(1) 5998. doi:https://doi.org/10.1207/s1532690xci0601_3

    • Search Google Scholar
    • Export Citation
  • 26.

    LakoffG & JohnsonM (2003). Metaphors we live by. Chicago, IL: University of Chicago Press. doi:https://doi.org/10.7208/chicago/9780226470993.001.0001

    • Search Google Scholar
    • Export Citation
  • 27.

    LamonSJ (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In LesterFKJr (Ed.) Second handbook of research on mathematics teaching and learning (pp. 629667). Charlotte, NC: Information Age.

    • Search Google Scholar
    • Export Citation
  • 28.

    LeungC (2005). Mathematical vocabulary: Fixers of knowledge or points of exploration? Language and Education19(2) 126134. doi:https://doi.org/10.1080/09500780508668668

    • Search Google Scholar
    • Export Citation
  • 29.

    LinebackJE (2015). The redirection: An indicator of how teachers respond to student thinking. Journal of the Learning Sciences24(3) 419460. doi:https://doi.org/10.1080/10508406.2014.930707

    • Search Google Scholar
    • Export Citation
  • 30.

    LiversSD & Bay-WilliamsJM (2014). Vocabulary support: Constructing (not obstructing) meaning. Mathematics Teaching in the Middle School20(3) 152159. doi:https://doi.org/10.5951/mathteacmiddscho.20.3.0152

    • Search Google Scholar
    • Export Citation
  • 31.

    McClainK & CobbP (2001). Supporting students’ ability to reason about data. Educational Studies in Mathematics45(1–3) 103129. doi:https://doi.org/10.1023/A:1013874514650

    • Search Google Scholar
    • Export Citation
  • 32.

    McKeownMGBeckILOmansonRC & PopleMT (1985). Some effects of the nature and frequency of vocabulary instruction on the knowledge and use of words. Reading Research Quarterly20(5) 522535. doi:https://doi.org/10.2307/747940

    • Search Google Scholar
    • Export Citation
  • 33.

    MilesMBHubermanAM & SaldañaJ (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Thousand Oaks, CA: Sage.

  • 34.

    MoschkovichJN (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. Journal of the Learning Sciences5(3) 239277. doi:https://doi.org/10.1207/s15327809jls0503_4

    • Search Google Scholar
    • Export Citation
  • 35.

    NacaratoAM & GrandoRC (2014). The role of language in building probabilistic thinking. Statistics Education Research Journal13(2) 93103. Retrieved from http://iase-web.org/documents/SERJ/SERJ13(2)_Nacarato.pdf

    • Search Google Scholar
    • Export Citation
  • 36.

    NagyWE & ScottJA (2000). Vocabulary processes. In KamilMLMosenthalPBPearsonPD & BarrR (Eds.) Handbook of reading research (Vol. III pp. 269284). Mahwah, NJ: Lawrence Erlbaum Associates.

    • Search Google Scholar
    • Export Citation
  • 37.

    National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

  • 38.

    National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

  • 39.

    National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author. Retrieved from http://www.corestandards.org/

    • Search Google Scholar
    • Export Citation
  • 40.

    NortonRM (2001). Determining probabilities by examining underlying structure. Mathematics Teaching in the Middle School7(2) 7882.

  • 41.

    PimmD (1987). Speaking mathematically: Communication in mathematics classrooms. London, UK: Routledge.

  • 42.

    PresmegNC (1998). Metaphoric and metonymic signification in mathematics. Journal of Mathematical Behavior17(1) 2532. doi:https://doi.org/10.1016/S0732-3123(99)80059-5

    • Search Google Scholar
    • Export Citation
  • 43.

    RubensteinRN (2007). Focused strategies for middle-grades mathematics vocabulary development. Mathematics Teaching in the Middle School13(4) 200207.

    • Search Google Scholar
    • Export Citation
  • 44.

    SchmittN (1998). Tracking the incremental acquisition of second language vocabulary: A longitudinal study. Language Learning48(2) 281317. doi:https://doi.org/10.1111/1467-9922.00042

    • Search Google Scholar
    • Export Citation
  • 45.

    ShaughnessyJM (2007). Research on statistics learning and reasoning. In LesterFKJr (Ed.) Second handbook of research on mathematics teaching and learning (pp. 9571009). Charlotte, NC: Information Age.

    • Search Google Scholar
    • Export Citation
  • 46.

    SieglerRS & CrowleyK (1991). The microgenetic method: A direct means for studying cognitive development. American Psychologist46(6) 606620. doi:https://doi.org/10.1037/0003-066X.46.6.606

    • Search Google Scholar
    • Export Citation
  • 47.

    SmitJ & van EerdeHAA (2011). A teacher’s learning process in dual design research: Learning to scaffold language in a multilingual mathematics classroom. ZDM–The International Journal on Mathematics Education43(6–7) 889900. doi:https://doi.org/10.1007/s11858-011-0350-5

    • Search Google Scholar
    • Export Citation
  • 48.

    TarrJE (2002). The confounding effects of “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics24(4) 3553.

    • Search Google Scholar
    • Export Citation
  • 49.

    ThompsonDR & RubensteinRN (2000). Learning mathematics vocabulary: Potential pitfalls and instructional strategies. Mathematics Teacher93(7) 568574.

    • Search Google Scholar
    • Export Citation
  • 50.

    WatsonJM (2005). The probabilistic reasoning of middle school students. In JonesGA (Ed.) Exploring probability in school: Challenges for teaching and learning (pp. 145169). New York, NY: Springer. doi:https://doi.org/10.1007/0-387-24530-8_7

    • Search Google Scholar
    • Export Citation
  • 51.

    WatsonJM (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum Associates.

  • 52.

    WatsonJM & MoritzJB (2002). School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology33(1) 5984. doi:https://doi.org/10.1080/00207390110087615

    • Search Google Scholar
    • Export Citation
  • 53.

    WatsonJM & MoritzJB (2003). The development of comprehension of chance language: Evaluation and interpretation. School Science and Mathematics103(2) 6580. doi:https://doi.org/10.1111/j.1949-8594.2003.tb18222.x

    • Search Google Scholar
    • Export Citation

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