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>JIO@SOP<GDU<>D_I� N@� D?@IODAD><I� GJN� >JI>@KOJN� H<O@HYOD>JN� T� >JIO@SOP<G@N� LP@� @IOM<I� @I� EP@BJ � O<G@N� >JHJ� @>P<>D_I� <GB@=M<D>< �@>P<>D_I�<GB@=M<D><� GDI@<G �NDNO@H<N�?@�@>P<>DJI@N �H\OJ?JN�?@� NJGP>D_I � =<G<I>@� ?@� H<O@MD< � >JI>@IOM<>DJI@N� T� H@U>G<N� ?@� NPNO<I>D<N� LP]HD><N�� Caracterización del proceso cognitivo de los estudiantes al resolver problemas contextualizados JHJ�N@�C<�M@A@MD?J�N@�OM<=<E_�>JI�PI�BMPKJ�?@�@IAJLP@�?@�@NOP?D<IO@N�?@G� -MJBM<H<�"?P><ODQJ� ?@� 1\>ID>J�2IDQ@MNDO<MDJ� @I�-MJ>@NJN��GDH@IO<MDJN�� )<� ><M<>O@MDU<>D_I� ?@G� KMJ>@NJ� >JBIDODQJ� N@� M@<GDU<� H@?D<IO@� @G� <IYGDNDN� ?@G� <>OP<M�?@�GJN�@NOP?D<IO@N�<�OM<Q\N�?@�G<N�M@KM@N@IO<>DJI@N�LP@�C<>@I�?@�GJN� DIQ<MD<IO@N� @I� GJN� @NLP@H<N� LP@� >JINOMPT@I � @I� K<MOD>PG<M � @G� @NLP@H<� ?@� @IO@I?DHD@IOJ�T�@G�@NLP@H<�?@�NJGP>D_I �N@B`I�GJ�LP@�KMJKJI@�#GJM@N��������� "I� N@BPD?<� N@� ?@N>MD=@I� GJN� M@NPGO<?JN� J=O@ID?JN� ?@NKP\N� ?@� <I<GDU<M� GJN� ?J>PH@IOJN�@N>MDOJN�T�G<N�ADGH<>DJI@N�?@G�<>OP<M�?@G�BMPKJ�?@�@IAJLP@�� �Q<I>@N�@I�*<O@HYOD><�"?P><ODQ<��1@>IJGJB]<�T�H<O@HYOD><N� 191" " a) Adaptación de esquemas de entendimiento y solución !PM<IO@� @G� <IYGDNDN� ?@� M@NPGO<?JN� N@� C<� QDNOJ� G<� I@>@ND?<?� ?@� <?<KO<M� G<� KMJKP@NO<� ?@� GJN� @NLP@H<N� ?@� @IO@I?DHD@IOJ� T� NJGP>D_I� ?@� #GJM@N� ������� ?<?J� LP@� @NOJN� C<I� ND?J� DINPAD>D@IO@N� <IO@� G<� NJGP>D_I� ?@� � GJN� KMJ=G@H<N� H<O@HYOD>JN�>JIO@SOP<GDU<?JN��� "I�<O@I>D_I�>JI�GJ�<IO@MDJM �@I�G<N�><O@BJM]<N�M@NPGO<IO@N�?@�G<�DIQ@NODB<>D_I� N@�D?@IODAD><I�� �� 2I� @NLP@H<� ?@� entendimiento canónico, @I� @G� LP@� N@� J=N@MQ<� G<� >JHKM@IND_I �KJM�K<MO@�?@G�BMPKJ�?@�@IAJLP@ �?@�G<�NDOP<>D_I�KMJ=G@H<� PODGDU<I?J�?@�AJMH<�<?@>P<?J�GJN�KMJK_NDOJN �G<N�M@BG<N�?@�<>>D_I �G<N� DIA@M@I>D<N�T�G<N�M@KM@N@IO<>DJI@N�?@�GJN�DIQ<MD<IO@N�JK@M<OJMDJN��� �� 2I�esquema algorítmico �K@MHDO@�LP@�@G�BMPKJ�?@�@IAJLP@�M@>PMM<�<� G<� NDH=JGDU<>D_I�T�@G� KMJ>@?DHD@IOJ�>JIQ@I>DJI<G�?@G�H@><IDNHJ�LP@� N@� Q<� <� N@BPDM� K<M<� ?<M� NJGP>D_I� <� G<� NDOP<>D_I� KMJ=G@H<�� "I� G<� DIQ@NODB<>D_I�N@�?DNODIBP@�� Aritmético, @N� >P<I?J� N@� C<>@�PNJ� ?@� JK@M<>DJI@N� <MDOH\OD><N� K<M<�G<�M@NJGP>D_I�?@�G<N�NDOP<>DJI@N�@I�>JIO@SOJ�� Algebraico � D?@IODAD><?J�>P<I?J�N@� M@>PMM@�<� G<�IJO<>D_I�KMJKD<� ?@G� G@IBP<E@� <GB@=M<D>J� @I� G<� NJGP>D_I� ?@� G<N� NDOP<>DJI@N� KG<IO@<?<N�� JIN@>P@IO@H@IO@ � NPMB@I� G<N� ><O@BJM]<N� ?@� M@KM@N@IO<>D_I� ><I_ID><� <GBJM]OHD>< � ><I_ID><� <GBJM]OHD><� <MDOH\OD><� T� ><I_ID><� <GBJM]OHD><� <GB@=M<D><���� b) Identificación de representaciones propias del contexto !PM<IO@� G<N� <>ODQD?<?@N� @I� G<N� NDOP<>DJI@N� KMJ=G@H<N� LP@� NPMB@I� ?@� G<� >JIO@SOP<GDU<>D_I� ?@� NDNO@H<N� ?@� @>P<>DJI@N� <GB@=M<D><N� GDI@<G@N� >JI� @G� =<G<I>@� ?@� H<O@MD< � N@� ?@O@>O_� @I� @G� <>OP<M� ?@� GJN� @NOP?D<IO@N � @G� PNJ� M@>PMM@IO@� ?@� ?DA@M@IO@N� ODKJN� ?@� M@KM@N@IO<>DJI@N� LP@� N@� >JIND?@M<I� @NK@>]AD><N� T� KMJKD<N� ?@� G<� QDI>PG<>D_I� ?@� ?JN� YM@<N� ?@G� >JIJ>DHD@IOJ � @N� ?@>DM �LP@�KP@?@I�J�IJ�NPMBDM�@I�JOM<N�QDI>PG<>DJI@N�� �Q<I>@N�@I�*<O@HYOD><�"?P><ODQ<��1@>IJGJB]<�T�H<O@HYOD><N� 192" " -JM� >JINDBPD@IO@ � <?@HYN� ?@� G<N� ><O@BJM]<N� ?@� M@KM@N@IO<>D_I� <I<GDU<?<N� >JI� G<� >G<NDAD><>D_I� ?@� #GJM@N � T� KJM� G<� DHKJMO<I>D<� LP@� OPQD@MJI� G<N� M@KM@N@IO<>DJI@N�@I>JIOM<?<N�K<M<� G<�>JINOMP>>D_I�?@G�>JIJ>DHD@IOJ�?@�?JN� >D@I>D<N� QDI>PG<?<N � AP@� I@>@N<MDJ� ?@ADIDM� PI<� >G<NDAD><>D_I� ?@� GJN� ODKJN� ?@� M@KM@N@IO<>DJI@N�@I>JIOM<?JN �LP@?<I?J�?@N>MDO<N�>JHJ�<�ODKJ�KMJKJND>DJI<G� �-���=�ODKJ� ADBPM<ODQ<�IJ�JK@M<ODQ<� �#+,���>�� ODKJ� ADBPM<ODQ<�JK@M<ODQ<� �#,���?�� ODKJ� <I<G_BD><� ��+�� T� @�� ODKJ� NDH=_GD><� H<O@HYOD><� �*��� )<� `GODH< � >JIND?@M<?<� >JHJ� G<� M@KM@N@IO<>D_I� LP@� K@MHDO@� G<� <KM@C@IND_I� ?@G� >JIJ>DHD@IOJ� H<O@HYOD>J� ?@� DIO@M\N� N@� ><M<>O@MDU_� KJM� ?DNODIBPDM� OM@N� KMJ>@NJN�K<M<�NP�>JINOMP>>D_I�����-MJ>@NJ�?@�DIO@MKM@O<>D_I�T�N@G@>>D_I�?@�G<� DIAJMH<>D_I�����-MJ>@NJ�?@�@NOMP>OPM<>D_I�T����-MJ>@NJ�?@�JK@M<>DJI<GDU<>D_I��� c) Procesos cognitivo al resolver problemas matemáticos contextualizados )JN� M@NPGO<?JN� J=O@ID?JN� K@MHDOD@MJI� @G<=JM<M� PI<� @N><G<� ?@� ?@N<MMJGGJ� >JBIDODQJ� @I� GJN� @NOP?D<IO@N� <IO@� G<� NJGP>D_I� ?@� KMJ=G@H<N� H<O@HYOD>JN� >JIO@SOP<GDU<?JN��ADBPM<��� �>JHKMJ=<I?J�GJ�M@A@MD?J�KJM�3@MBI<?�@I�M@G<>D_I� <G� ?JHDIDJ� BM<?P<G� ?@� GJN� >JIJ>DHD@IOJN��� � � � � � � � � #DBPM<����!JHDIDJ�BM<?P<G�?@G�><HKJ�>JI>@KOP<G�?@�PI�NDNO@H<�?@� @>P<>DJI@N�<GB@=M<D>J�GDI@<G�@I�@G�>JIO@SOJ�?@�PI�=<G<I>@�?@�H<O@MD<�� �Q<I>@N�@I�*<O@HYOD><�"?P><ODQ<��1@>IJGJB]<�T�H<O@HYOD><N� 193" " #P@IO@��!DN@^J�KMJKDJ��������� � d) Sobre las representaciones de los invariantes operatorios que caracterizan el desarrollo del proceso cognitivo. )<� NJGP>D_I� @SK@MO<� T� KJM� O<IOJ� @G� ?JHDIDJ� ?@G� ><HKJ� >JI>@KOP<G� N@� ?<� >P<I?J� @G� BMPKJ� ?@� @IAJLP@� @IOD@I?@ � @NOMP>OPM<� T� ?JHDI<� GJN� DIQ<MD<IO@N� 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?@� H<I@M<� @NKJIOYI@<� ?PM<IO@� @G� <>OP<M�?@�GJN�@NOP?D<IO@N��� 0D� =D@I� <G� ADI<G� ?@� G<N� N@NDJI@N� GJN� @NOP?D<IO@N� ?DNKJI@I� ?@� @NLP@H<N� <KMJKD<?JN�K<M<�@IAM@IO<M�@Q@IOJN�>JIO@SOP<GDU<?JN�LP@� M@LPD@M@I�NDNO@H<N� ?@� @>P<>DJI@N� <GB@=M<D><N� GDI@<G@N � @N� I@>@N<MDJ� @SKGJM<M� HYN� <>@M><� ?@� @NOJ �NJ=M@�OJ?J�@I�>JIO@SOJN�?DA@M@IO@N�� REFERENCIAS <H<M@I< �$��-�� ������ � k"G�>PMM]>PGJ�?@� G<N�H<O@HYOD><N�@I� DIB@ID@M]<l �@I� Memorias de las Mesas redondas sobre definición de líneas de investigación en el IPN, *\SD>J�� �Q<I>@N�@I�*<O@HYOD><�"?P><ODQ<��1@>IJGJB]<�T�H<O@HYOD><N� 194" " <H<M@I< �$��-�� ������ � k)<�@IN@^<IU<�?@� G<N�H<O@HYOD><N�@I�@G�>JIO@SOJ� ?@�G<�DIB@ID@M]<l �KJI@I>D<�KM@N@IO<?<�@I�@G�553&&&� JIBM@NJ�+<>DJI<G� ?@� G<� 0J>D@?<?� *<O@HYOD><� *@SD><I< � *\SD>J�� <H<M@I< � $�� -�� ������ � &IAJMH@� ?@G� KMJT@>OJ� ?@� DIQ@NODB<>D_I� ODOPG<?J�� k"O<K<N� ?@� G<� H<O@HYOD><�@I�@G�>JIO@SOJ�?@�G<�DIB@ID@M]<l �*\SD>J �"0&*"�&-+�� !PQ<G � /�� ������ � k0@HDJNDN� T� IJ@NDNl � @I� "��0YI>C@U� T� $�� 7P=D@O<� �@?N�� � Lecturas en didáctica de la matemática: Escuela Francesa, *\SD>J � 0@>>D_I�?@�*<O@HYOD><�"?P><ODQ<�?@G� &+3"01�3�&-+ �KK����������� #@P@MNO@DI � /� � 6�� /<I? � *�� ��� %JAAH<I� T� /�� *DGG@M� ������ � Instrumental Enrichment, �<GODHJM@ �2IDQ@MNDOT�-<MF�-M@NN�� #GJM@N � /�� ������ � El conocimiento matemático en problemas de adición y sustracción: un estudio sobre las relaciones entre conceptos, esquemas y representación, 1@NDN� ?@� !J>OJM<?J� @I� "?P><>D_I � �BP<N><GD@IO@N ��BN� �*\SD>J�� -D<B@O � '�� ������ � Introducción a la epistemología genética, el pensamiento matemático, "NK<^< �-<D?_N��-ND>JGJB]<�"QJGPODQ<��� 1M@EJ � 1�� "��� <H<M@I< � $�� -�� �������� �IYGDNDN� >JBIDODQJ� ?@� NDOP<>DJI@N� KMJ=G@H<�>JI�NDNO@H<N�?@�@>P<>DJI@N�<GB@=M<D><N�@I�@G�>JIO@SOJ�?@G� =<G<I>@�?@�H<O@MD<��"?P><>D_I�*<O@HYOD><��3JG����+`H��� �KK�������� $MPKJ�0<IODGG<I< �*\SD>J�� 3@MB<IP? �$�������� �El niño, las matemáticas y la realidad: problemas de la enseñanza de las matemáticas en la escuela primaria, *\SD>J �1MDGG<N�� 3@MB<IP? � $�� ������ � k1C@� 1C@JMT� JA� JI>@KOP<G� #D@G?Nl � @I� )�� 0O@OO@ � -�� +@NC@M � -�� J== � $�� ��� $JG?DI� T� ��� $M@@M� �@?N�� � Theories of Mathematical Learning, *<CR<C �+' �)<RM@I>@�"MG=<PH �KK����������� � �Q<I>@N�@I�*<O@HYOD><�"?P><ODQ<��1@>IJGJB]<�T�H<O@HYOD><N�