Not All Opportunities to Prove are the Same

Confusion can arise from the subtle difference between proving a general and a particular statement, especially when general statements are presented by textbooks in ways that make them appear particular in nature. The authors discuss the implications for teaching proof in light of the current oppor...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Mathematics teacher 2013-09, Vol.107 (2), p.138-142
Hauptverfasser: Gilbertson, Nicholas J, Otten, Samuel, Males, Lorraine M, Clark, D. Lee
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 142
container_issue 2
container_start_page 138
container_title The Mathematics teacher
container_volume 107
creator Gilbertson, Nicholas J
Otten, Samuel
Males, Lorraine M
Clark, D. Lee
description Confusion can arise from the subtle difference between proving a general and a particular statement, especially when general statements are presented by textbooks in ways that make them appear particular in nature. The authors discuss the implications for teaching proof in light of the current opportunities in high school geometry textbooks.
doi_str_mv 10.5951/mathteacher.107.2.0138
format Article
fullrecord <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_1433367142</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ericid>EJ1034790</ericid><jstor_id>10.5951/mathteacher.107.2.0138</jstor_id><sourcerecordid>10.5951/mathteacher.107.2.0138</sourcerecordid><originalsourceid>FETCH-LOGICAL-e942-4427cef2a28003adc18fe828be55b7534e6da2bdfb4ad7dd436e6dcc9f281f023</originalsourceid><addsrcrecordid>eNpNkF1Lw0AQRRdRsFZ_grLgoyTOfmU3j6W0flCsYN-XTTKhKUk3braC_96UijgvA_ceZuAQcscgVblij52L24iu3GJIGeiUp8CEOSMTLgQkoAw_JxMArhKls_ySXA3DDsaRBibk4c1HOmtbuu57H-Jh38QGBxo9fQ_-C6kLSOMW6Yfr8Jpc1K4d8OZ3T8lmudjMn5PV-ullPlslmEueSMl1iTV33AAIV5XM1Gi4KVCpQishMascL6q6kK7SVSVFNiZlmdfcsBq4mJL709k--M8DDtHu_CHsx4-WSSFEppk8UrcnCkNT2j40nQvfdvHKQEidw9iLU78bog9_AAN7lGb_SRszbbk9ShM_rCpg2g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1433367142</pqid></control><display><type>article</type><title>Not All Opportunities to Prove are the Same</title><source>JSTOR Mathematics &amp; Statistics</source><source>Jstor Complete Legacy</source><creator>Gilbertson, Nicholas J ; Otten, Samuel ; Males, Lorraine M ; Clark, D. Lee</creator><creatorcontrib>Gilbertson, Nicholas J ; Otten, Samuel ; Males, Lorraine M ; Clark, D. Lee</creatorcontrib><description>Confusion can arise from the subtle difference between proving a general and a particular statement, especially when general statements are presented by textbooks in ways that make them appear particular in nature. The authors discuss the implications for teaching proof in light of the current opportunities in high school geometry textbooks.</description><identifier>ISSN: 0025-5769</identifier><identifier>EISSN: 2330-0582</identifier><identifier>DOI: 10.5951/mathteacher.107.2.0138</identifier><identifier>CODEN: MATAAP</identifier><language>eng</language><publisher>Reston: National Council of Teachers of Mathematics (NCTM)</publisher><subject>Connecting Research to teaching ; Deductive reasoning ; Geometry ; High School Students ; High schools ; Logical Thinking ; Mathematical Logic ; Mathematical problems ; Mathematics education ; Mathematics Instruction ; Mathematics teachers ; Proof theory ; Reasoning ; Secondary school curricula ; Secondary School Mathematics ; Secondary school students ; Textbooks ; Triangles ; Validity</subject><ispartof>The Mathematics teacher, 2013-09, Vol.107 (2), p.138-142</ispartof><rights>Copyright 2013 National Council of Teachers of Mathematics, Inc.</rights><rights>Copyright National Council of Teachers of Mathematics Sep 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,800,829,27905,27906</link.rule.ids><backlink>$$Uhttp://eric.ed.gov/ERICWebPortal/detail?accno=EJ1034790$$DView record in ERIC$$Hfree_for_read</backlink></links><search><creatorcontrib>Gilbertson, Nicholas J</creatorcontrib><creatorcontrib>Otten, Samuel</creatorcontrib><creatorcontrib>Males, Lorraine M</creatorcontrib><creatorcontrib>Clark, D. Lee</creatorcontrib><title>Not All Opportunities to Prove are the Same</title><title>The Mathematics teacher</title><description>Confusion can arise from the subtle difference between proving a general and a particular statement, especially when general statements are presented by textbooks in ways that make them appear particular in nature. The authors discuss the implications for teaching proof in light of the current opportunities in high school geometry textbooks.</description><subject>Connecting Research to teaching</subject><subject>Deductive reasoning</subject><subject>Geometry</subject><subject>High School Students</subject><subject>High schools</subject><subject>Logical Thinking</subject><subject>Mathematical Logic</subject><subject>Mathematical problems</subject><subject>Mathematics education</subject><subject>Mathematics Instruction</subject><subject>Mathematics teachers</subject><subject>Proof theory</subject><subject>Reasoning</subject><subject>Secondary school curricula</subject><subject>Secondary School Mathematics</subject><subject>Secondary school students</subject><subject>Textbooks</subject><subject>Triangles</subject><subject>Validity</subject><issn>0025-5769</issn><issn>2330-0582</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNpNkF1Lw0AQRRdRsFZ_grLgoyTOfmU3j6W0flCsYN-XTTKhKUk3braC_96UijgvA_ceZuAQcscgVblij52L24iu3GJIGeiUp8CEOSMTLgQkoAw_JxMArhKls_ySXA3DDsaRBibk4c1HOmtbuu57H-Jh38QGBxo9fQ_-C6kLSOMW6Yfr8Jpc1K4d8OZ3T8lmudjMn5PV-ullPlslmEueSMl1iTV33AAIV5XM1Gi4KVCpQishMascL6q6kK7SVSVFNiZlmdfcsBq4mJL709k--M8DDtHu_CHsx4-WSSFEppk8UrcnCkNT2j40nQvfdvHKQEidw9iLU78bog9_AAN7lGb_SRszbbk9ShM_rCpg2g</recordid><startdate>20130901</startdate><enddate>20130901</enddate><creator>Gilbertson, Nicholas J</creator><creator>Otten, Samuel</creator><creator>Males, Lorraine M</creator><creator>Clark, D. Lee</creator><general>National Council of Teachers of Mathematics (NCTM)</general><general>National Council of Teachers of Mathematics</general><scope>7SW</scope><scope>BJH</scope><scope>BNH</scope><scope>BNI</scope><scope>BNJ</scope><scope>BNO</scope><scope>ERI</scope><scope>PET</scope><scope>REK</scope><scope>WWN</scope><scope>JQ2</scope></search><sort><creationdate>20130901</creationdate><title>Not All Opportunities to Prove are the Same</title><author>Gilbertson, Nicholas J ; Otten, Samuel ; Males, Lorraine M ; Clark, D. Lee</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-e942-4427cef2a28003adc18fe828be55b7534e6da2bdfb4ad7dd436e6dcc9f281f023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Connecting Research to teaching</topic><topic>Deductive reasoning</topic><topic>Geometry</topic><topic>High School Students</topic><topic>High schools</topic><topic>Logical Thinking</topic><topic>Mathematical Logic</topic><topic>Mathematical problems</topic><topic>Mathematics education</topic><topic>Mathematics Instruction</topic><topic>Mathematics teachers</topic><topic>Proof theory</topic><topic>Reasoning</topic><topic>Secondary school curricula</topic><topic>Secondary School Mathematics</topic><topic>Secondary school students</topic><topic>Textbooks</topic><topic>Triangles</topic><topic>Validity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gilbertson, Nicholas J</creatorcontrib><creatorcontrib>Otten, Samuel</creatorcontrib><creatorcontrib>Males, Lorraine M</creatorcontrib><creatorcontrib>Clark, D. Lee</creatorcontrib><collection>ERIC</collection><collection>ERIC (Ovid)</collection><collection>ERIC</collection><collection>ERIC</collection><collection>ERIC (Legacy Platform)</collection><collection>ERIC( SilverPlatter )</collection><collection>ERIC</collection><collection>ERIC PlusText (Legacy Platform)</collection><collection>Education Resources Information Center (ERIC)</collection><collection>ERIC</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Mathematics teacher</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gilbertson, Nicholas J</au><au>Otten, Samuel</au><au>Males, Lorraine M</au><au>Clark, D. Lee</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><ericid>EJ1034790</ericid><atitle>Not All Opportunities to Prove are the Same</atitle><jtitle>The Mathematics teacher</jtitle><date>2013-09-01</date><risdate>2013</risdate><volume>107</volume><issue>2</issue><spage>138</spage><epage>142</epage><pages>138-142</pages><issn>0025-5769</issn><eissn>2330-0582</eissn><coden>MATAAP</coden><abstract>Confusion can arise from the subtle difference between proving a general and a particular statement, especially when general statements are presented by textbooks in ways that make them appear particular in nature. The authors discuss the implications for teaching proof in light of the current opportunities in high school geometry textbooks.</abstract><cop>Reston</cop><pub>National Council of Teachers of Mathematics (NCTM)</pub><doi>10.5951/mathteacher.107.2.0138</doi><tpages>5</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0025-5769
ispartof The Mathematics teacher, 2013-09, Vol.107 (2), p.138-142
issn 0025-5769
2330-0582
language eng
recordid cdi_proquest_journals_1433367142
source JSTOR Mathematics & Statistics; Jstor Complete Legacy
subjects Connecting Research to teaching
Deductive reasoning
Geometry
High School Students
High schools
Logical Thinking
Mathematical Logic
Mathematical problems
Mathematics education
Mathematics Instruction
Mathematics teachers
Proof theory
Reasoning
Secondary school curricula
Secondary School Mathematics
Secondary school students
Textbooks
Triangles
Validity
title Not All Opportunities to Prove are the Same
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T09%3A45%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Not%20All%20Opportunities%20to%20Prove%20are%20the%20Same&rft.jtitle=The%20Mathematics%20teacher&rft.au=Gilbertson,%20Nicholas%20J&rft.date=2013-09-01&rft.volume=107&rft.issue=2&rft.spage=138&rft.epage=142&rft.pages=138-142&rft.issn=0025-5769&rft.eissn=2330-0582&rft.coden=MATAAP&rft_id=info:doi/10.5951/mathteacher.107.2.0138&rft_dat=%3Cjstor_proqu%3E10.5951/mathteacher.107.2.0138%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1433367142&rft_id=info:pmid/&rft_ericid=EJ1034790&rft_jstor_id=10.5951/mathteacher.107.2.0138&rfr_iscdi=true