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ze#k0dV$;44cFdp2`l}UJ>P8AzCWjzTlseF|Cl*hZR_`%Ro9m+zpCvO7PT6}@gharfSdz2+0yYkqCe{xoCq{6E5#zha+6MnC!f^ThnW6Q8Fm>+kzI z_wU^jhQ5Oq71F{6oS-Dov_Hk~u*n&Q$d(;1kF%QbZV}8-p5Us`?I6~u!xY(~6Tx-U zfu~VHg2|92iQ|YshoXS9LYo86LXXSxdB;}k{?Yl*yhrZXy6HR}EHb>tM&_m#CS0nj IuKsRZ04eY#jQ{`u diff --git a/doc/main.tex b/doc/main.tex index a87026b..060301f 100644 --- a/doc/main.tex +++ b/doc/main.tex @@ -44,7 +44,7 @@ \fancyhf{} % Wyczyść nagłówki i stopki \fancyhf{} % Wyczyść wszystkie pola nagłówka i stopki -\fancyhead[L]{\textbf{Szczegółowe Ocenianie z \textcolor{przedmiot}{Matematyki}}} % Lewa strona nagłówka: tytuł dokumentu +\fancyhead[L]{\textbf{DRAFT: Szczegółowe Ocenianie z \textcolor{przedmiot}{Matematyki}}} % Lewa strona nagłówka: tytuł dokumentu \fancyhead[C]{--~\thepage~--} % Środek nagłówka: numer strony \fancyhead[R]{\small \textcolor{zakres}{Zakres Rozsz.}, \textcolor{poziom}{Poziom 1}, M. Markiewicz, J. Góra} % Prawa strona nagłówka: dodatkowe informacje % \fancyhead[R]{\small \textcolor{zakres}{Zakres Rozszerzony}, \textcolor{poziom}{Poziom Nauczania: 1}} % Prawa strona nagłówka: dodatkowe informacje @@ -336,7 +336,6 @@ \end{longenum} \end{longenum} -\newpage \paragraf{Przedmiot Regulacji Szczegółowego Oceniania} \begin{longenum} @@ -359,169 +358,197 @@ \end{longenum} \end{longenum} - +% ------------------------------- %-------------------------------- \newpage -\section{Punktacja wymagań i minimalna liczba punktów} +\section{Punktacja i Przyznawanie Wag} -\paragraf{Cel i zakres punktacji wymagań i minimalnej liczby punktów} +\paragraf{Przedmito Regulacji: Punktacji i Przyznawania Wag} \begin{longenum} - - \item Celem tak ustalonej punktacji jest \textbf{określenie wagi poszczególnych wymagań} - w procesie oceniania oraz zapewnienie \emph{rzetelnego} odniesienia do treści programowych. %wynikających z podstawy programowej. - - \item \textbf{Minimalną liczbę punktów} \(\,(P_{\min})\) ustala się w celu wyznaczenia - progu \emph{pełnej realizacji} wymaganych treści wynikających z \textbf{PP}\footnotemark[2] dla danego \textcolor{poziom}{poziomu nauczania} w~zadanym zakresie, + \item Celem punktacji jest \textbf{określenie wagi poszczególnych wymagań} w procesie oceniania oraz zapewnienie \emph{rzetelnego} odniesienia do treści programowych. + \item \textbf{Minimalną liczbę punktów} (\(P_{\min}\)) ustala się w celu wyznaczenia progu \emph{pełnej realizacji} wymaganych treści wynikających z \textbf{PP}\footnotemark[2] dla danego \textcolor{poziom}{poziomu nauczania} w~zadanym zakresie, przy założeniu, że zostają spełnione wszystkie: \begin{itemize}[noitemsep] \item \textbf{Wymagania Szczegółowe}. \item \textbf{Wymagania Ogólne}. - % \item nie dochodzi do \textbf{wielokrotnego naliczania} tego samego WO, nawet jeśli jest ono powiązane z kilkoma WS. \end{itemize} - \end{longenum} -\paragraf{Punktacja wymagań} +\paragraf{Przypisywanie Wag do Wymagań} \begin{longenum} - \item Każdemu \textbf{Wymaganiu Szczegółowemu} (oznaczonemu indeksem \(i\)) przypisuje się - \textbf{wagę punktową} \(w_{s_i}\), przy czym minimalna wartość tej wagi wynosi 1. - - \item Każdemu \textbf{Wymaganiu Ogólnemu} (oznaczonemu indeksem \(j\)) przypisuje się - \textbf{wagę punktową} \(w_{o_j}\), przy czym minimalna wartość tej wagi wynosi 1. - - \item \textbf{Łączna liczba punktów} przysługujących danemu działowi określonemu w~\textbf{PP}\footnotemark[2], uwzględniająca wszystkie powiązania - między Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi, obliczana jest według następującej formuły: - - % \begin{equation} - % P_{\text{sum}} - % = - % \sum_{i=1}^{N_{W_S}} - % \Bigl( - % w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} - % \Bigr), - % \label{wzor:punktacja} - % \end{equation} - % gdzie: - % \begin{itemize}[noitemsep] - % \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w danym dziale, - % \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z \(i\)-tym Wymaganiem Szczegółowym. - % \end{itemize} - - \begin{equation} - P_{\text{sum}} = \sum_{i=1}^{N_{W_S}} \Bigl( w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} \Bigr) - \label{wzor:punktacja} - \end{equation} - - gdzie: - \begin{itemize}[noitemsep] - \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w~danym dziale, - \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z~\(i\)-tym Wymaganiem Szczegółowym, - \item \(N^i_{W_O} \geq 1\) dla każdego \(i\). - \end{itemize} - - {\small - \textbf{Uwaga:} Wzór (\ref{wzor:punktacja}) służy do określenia \emph{całkowitej} liczby punktów możliwej - do uzyskania za pełne zrealizowanie danego działu, z uwzględnieniem konkretnych - powiązań pomiędzy Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi. - } - - \item Celem tak ustalonej punktacji jest określenie wagi poszczególnych wymagań edukacyjnych - w~procesie oceniania osiągnięć edukacyjnych. - - \item \textbf{Punktacja} przypisana poszczególnym działom oraz łączna liczba punktów - \(\bigl(P_{\text{sum}}\bigr)\), obliczona zgodnie ze wzorem~(\ref{wzor:punktacja}), - znajduje się w~\textbf{Rozdziale~1~załącznika~1}. - + \item Każdemu \textbf{wymaganiu szczegółowemu} przypisuje się wagę \(w_{s_i}\), gdzie \(i\) to indeks wymaganego szczegółowego. + \item Każdemu \textbf{wymaganiu ogólnemu} przypisuje się wagę \(w_{o_j}\), gdzie \(j\) to indeks wymaganego ogólnego. + \item Wagi są ustalane w oparciu o ich znaczenie w programie nauczania i mogą przyjmować wartości całkowite lub ułamkowe. \end{longenum} -\paragraf{Ustalanie minimalnej liczby punktów} +\paragraf{Punktacja dla Zadań} \begin{longenum} - \item \textbf{Minimalną liczbę punktów} \(P_{\min}\) opisaną wzorem (\ref{eq:pmin}) ustala się w celu wyznaczenia - progu \emph{pełnej realizacji} wymaganych treści wynikających z~\textbf{PP}\footnotemark[2]. - -\begin{equation} - P_{\min} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\} - \label{eq:pmin} - \end{equation} - Gdzie: - \begin{itemize} - \item \( P_{\min} \) to minimalna wartość całkowitej punktacji, - \item \( N_{W_S} \) to liczba wymagań szczegółowych, - \item \( w_{s_i} \) to waga \( i \)-tego wymagania szczegółowego, - \item \( w_{o_j(i)} \) to waga wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego, - \item \( j(i) \) to indeks wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego. - \end{itemize} - - \begin{equation} - \forall i \in \{1, \dots, N_{W_S}\}, \quad \exists j(i) \in \{1, \dots, N_{W_O}^i\} - \label{eq:warunek} - \end{equation} - Warunek określony wzorem (\ref{eq:warunek}) zapewnia, że dla każdego wymagania szczegółowego wybrane jest dokładnie jedno wymaganie ogólne, a jednocześnie wszystkie wymagania są zrealizowane. - - \textbf{Uwaga:} W przypadku, gdy każdemu Wymaganiu Szczegółowemu i Ogólnemu przypisuje się \textbf{1~punkt}, wówczas minimalna liczba punktów \( P_{\min} \) realizujących obowiązkowe wymagania edukacyjne z~podstawy programowej dla danego działu wyraża się wzorem (\ref{eq:min_points}). - - \begin{equation} - \label{eq:min_points} - P_{\min} = N_{W_S} - \end{equation} - - Gdzie \( N_{W_S} \) oznacza liczbę Wymagań Szczegółowych. - - \item Minimalna liczba punktów \(\bigl(P_{\text{sum}}\bigr)\) realizująca obowiązkowe wymagania zgodnie z \textbf{PP}\footnotemark[2], znajduje się w~\textbf{Rozdziale~1~załącznika~1}. - -\end{longenum} - -%--------------------------------- -\newpage -\section{Punktacja Osiągnięć Edukacyjnych} - -\paragraf{Cel i zakres punktacji osiągnięć edukacyjnych} -\begin{longenum} - \item Punktacja osiągnieć edukacyjnych, określona niniejszym przepisem, służy do dokonywania oceny osiągnięć edukacyjnych, realizowanych zgodnie z zasadami zawartymi w \textbf{Szczegółowym Ocenianiu}, opartymi na kryteriach stanowiących integralną część \textbf{Wewnątrzszkolnego Oceniania}. - - \item Każde zadanie stanowi integralny element systemu oceny, przy czym realizacja co najmniej jednego \textbf{Wymagania Szczegółowego} przypisanego co najmniej jednemu \textbf{Wymaganiu Ogólnemu} jest warunkiem koniecznym. - - \item Ocena zadania ustalana jest na podstawie procentowego udziału punktów zdobytych przez ucznia w stosunku do maksymalnej liczby punktów możliwych do uzyskania przy realizacji danego zadania. -\end{longenum} - -\paragraf{Punktowanie zadania} -\begin{longenum} - \item Zadanie podlega ocenie według kryterium procentowej realizacji wymagań, przy czym procentowe progi przyznawania poszczególnych ocen ustalono zgodnie z wytycznymi określonymi w systemie \textbf{Wewnątrzszkolnego Oceniania (WO)}. - - \item Każdemu z wymagań, zarówno ogólnym, jak i szczegółowym, przypisano określoną wagę, która wyznacza jego znaczenie w procesie oceny zadania. - - \item Łączna liczba punktów przypisywana zadaniu stanowi sumę punktów przyznanych za realizację poszczególnych wymagań, przy czym uzyskanie oceny pozytywnej wymaga realizacji co najmniej jednego \textbf{Wymagania Szczegółowego} oraz osiągnięcia minimalnego progu punktowego. - - \item Procentowy udział zdobytych punktów oblicza się według wzoru: + \item Punktacja zadania obliczana jest na podstawie realizacji poszczególnych wymagań szczegółowych i ogólnych. + \item Maksymalna liczba punktów za zadanie (\(P_{\text{zad}}\)) wyznaczana jest jako suma wag wszystkich realizowanych wymagań: \begin{equation} - \% = \frac{\sum_{i=1}^{n} p_i}{\sum_{i=1}^{n} P_i} \times 100\% - \label{wzor:procent} + P_{\text{zad}} = \sum_{i=1}^{N_{W_S}} \Bigl( w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} \Bigr), + \label{eq:punktacja_zadania} \end{equation} gdzie: - \begin{longenum} - \item \(p_i\) – liczba punktów zdobytych za realizację \(i\)-tego wymagania, - \item \(P_i\) – maksymalna liczba punktów przypisana do \(i\)-tego wymagania. - \end{longenum} - - \item Ocena końcowa zadania, zwana dalej „oceną”, ustalana jest według następujących progów: - \begin{longenum} - \item \textbf{Ocena 6 (celująca)} – przyznawana w przypadku uzyskania co najmniej 95\% maksymalnej liczby punktów, - \item \textbf{Ocena 5 (bardzo dobra)} – przyznawana w przypadku uzyskania co najmniej 80\% maksymalnej liczby punktów, - \item \textbf{Ocena 4 (dobra)} – przyznawana w przypadku uzyskania co najmniej 65\% maksymalnej liczby punktów, - \item \textbf{Ocena 3 (dostateczna)} – przyznawana w przypadku uzyskania co najmniej 50\% maksymalnej liczby punktów, - \item \textbf{Ocena 2 (dopuszczająca)} – przyznawana w przypadku uzyskania co najmniej 30\% maksymalnej liczby punktów, - \item \textbf{Ocena 1 (niedostateczna)} – przyznawana w przypadku uzyskania wyniku niższego niż 30\% maksymalnej liczby punktów. - \end{longenum} - - \item Ustalenie oceny, zwanej dalej „daną oceną”, następuje w sytuacji, gdy osiągnięty zostanie minimalny próg realizacji zarówno \textbf{Wymagań Ogólnych}, jak i \textbf{Wymagań Szczegółowych}, określony w niniejszym przepisie. W szczególności: - \begin{longenum} - \item Aby przyznać ocenę \textbf{3 (dostateczną)}, wymagane jest zrealizowanie co najmniej 50\% wymagań przypisanych do zadania. - \item W odniesieniu do pozostałych ocen, minimalny procent realizacji wymagań musi być równy lub przekraczać progi określone w odpowiednich punktach. - \end{longenum} - - \item W przypadku stosowania dodatkowych progów lub wymogów, takich jak system „50 na 50”, warunki te muszą być wyraźnie określone w opisie kryteriów oceny zadania, a uczniowie powinni zostać o nich uprzednio poinformowani przed przystąpieniem do wykonania zadania. + \begin{itemize}[noitemsep] + \item \(N_{W_S}\) – liczba wymagań szczegółowych w zadaniu, + \item \(N^i_{W_O}\) – liczba wymagań ogólnych powiązanych z \(i\)-tym wymaganiem szczegółowym. + \end{itemize} \end{longenum} +\paragraf{Punktacja działów} + +\begin{longenum} + + \item \textbf{Ustalanie minimalnej liczby punktów}: + \begin{longenum} + \item Minimalną liczbę punktów \(P_{\min}\) opisaną wzorem (\ref{eq:pmin}) ustala się w celu wyznaczenia progu \emph{pełnej realizacji} wymaganych treści wynikających z~\textbf{PP}\footnotemark[2]. + \begin{equation} + P_{\min} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\}, + \label{eq:pmin} + \end{equation} + Gdzie: + \begin{itemize} + \item \(P_{\min}\) to minimalna wartość całkowitej punktacji, + \item \(N_{W_S}\) to liczba wymagań szczegółowych, + \item \(w_{s_i}\) to waga \(i\)-tego wymagania szczegółowego, + \item \(w_{o_j(i)}\) to waga wybranego wymagania ogólnego dla \(i\)-tego wymagania szczegółowego, + \item \(j(i)\) to indeks wybranego wymagania ogólnego dla \(i\)-tego wymagania szczegółowego. + \end{itemize} + \item Warunek określony wzorem (\ref{eq:warunek}) zapewnia, że dla każdego wymagania szczegółowego wybrane jest dokładnie jedno wymaganie ogólne, a jednocześnie wszystkie wymagania są zrealizowane: + \begin{equation} + \forall i \in \{1, \dots, N_{W_S}\}, \quad \exists j(i) \in \{1, \dots, N_{W_O}^i\}. + \label{eq:warunek} + \end{equation} + \item \textbf{Uwaga:} W przypadku, gdy każdemu Wymaganiu Szczegółowemu i Ogólnemu przypisuje się \textbf{1~punkt}, wówczas minimalna liczba punktów \(P_{\min}\) realizujących obowiązkowe wymagania edukacyjne z~podstawy programowej dla danego działu wyraża się wzorem (\ref{eq:min_points}): + \begin{equation} + \label{eq:min_points} + P_{\min} = N_{W_S}. + \end{equation} + Gdzie \(N_{W_S}\) oznacza liczbę Wymagań Szczegółowych. + \item Minimalna liczba punktów \(\bigl(P_{\text{sum}}\bigr)\) realizująca obowiązkowe wymagania zgodnie z \textbf{PP}\footnotemark[2], znajduje się w~\textbf{Rozdziale~1~załącznika~1}. + \end{longenum} + + + \item \textbf{Punktacja dla działów}: + \begin{longenum} + \item Punktacja dla danego działu (\(P_{\text{dział}}\)) obliczana jest jako suma maksymalnych punktów ze wszystkich zadań w ramach tego działu. + \item Maksymalna liczba punktów za dany dział (\(P_{\text{dział}}\)) wyznaczana jest według wzoru: + \begin{equation} + P_{\text{dział}} = \sum_{k=1}^{N_{\text{zad}}} P_{\text{zad}_k}, + \label{eq:punktacja_dzial} + \end{equation} + gdzie: + \begin{itemize}[noitemsep] + \item \(N_{\text{zad}}\) oznacza liczbę zadań w danym dziale, + \item \(P_{\text{zad}_k}\) to maksymalna liczba punktów za \(k\)-te zadanie w dziale. + \end{itemize} + \item Minimalna liczba punktów (\(P_{\min}^{\text{dział}}\)) potrzebna do zaliczenia działu wyznaczana jest według wzoru: + \begin{equation} + P_{\min}^{\text{dział}} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\}, + \label{eq:min_punkty_dzial} + \end{equation} + gdzie \(w_{o_j(i)}\) to waga jednego z wymagań ogólnych dla \(i\)-tego wymagania szczegółowego. + \end{longenum} + +\end{longenum} + +\paragraf{Punktacja dla Poziomu} +\begin{longenum} + \item Punktacja dla całego poziomu (\(P_{\text{poziom}}\)) obliczana jest jako suma maksymalnych punktów ze wszystkich działów: + \begin{equation} + P_{\text{poziom}} = \sum_{k=1}^{N_{\text{działa}}} P_{\min}^k, + \label{eq:punktacja_poziom} + \end{equation} + gdzie \(N_{\text{działa}}\) to liczba działów w ramach poziomu. +\end{longenum} + +\paragraf{Wyznaczenie Minimalnych i Maksymalnych Punktów} +\begin{longenum} + \item \textbf{Minimalne punkty dla zadań}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{zad}}\)) dla zadania to suma minimalnych wag wymagań niezbędnych do zaliczenia tego zadania. + \end{longenum} + \item \textbf{Minimalne punkty dla działów}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{dział}}\)) dla działu to suma minimalnych punktów z wszystkich zadań w ramach tego działu. + \end{longenum} + \item \textbf{Minimalne punkty dla poziomu}: + \begin{longenum} + \item Minimalna liczba punktów (\(P_{\min}^{\text{poziom}}\)) dla poziomu to suma minimalnych punktów z wszystkich działów w ramach tego poziomu. + \end{longenum} + \item \textbf{Maksymalne punkty}: + \begin{longenum} + \item Maksymalna liczba punktów (\(P_{\max}\)) dla zadań, działów i poziomu to odpowiednio sumy maksymalnych wag wszystkich wymagań. + \end{longenum} +\end{longenum} + +\newpage +\section{Przeliczenie Punktów na Oceny} + +\paragraf{Ocena za Zadanie} +\begin{longenum} + \item Ocena za zadanie ustalana jest na podstawie procentowego udziału zdobytych punktów (\(P_{\text{zdobyte}}\)) w stosunku do maksymalnej liczby punktów (\(P_{\text{max}}\)): + \begin{equation} + \% = \frac{P_{\text{zdobyte}}}{P_{\text{max}}} \times 100\%. + \label{eq:procent_zadanie} + \end{equation} + \item Progi ocen: + \begin{itemize}[noitemsep] + \item Ocena 6: min. 95\%, + \item Ocena 5: min. 80\%, + \item Ocena 4: min. 65\%, + \item Ocena 3: min. 50\%, + \item Ocena 2: min. 30\%, + \item Ocena 1: poniżej 30\%. + \end{itemize} +\end{longenum} + +\paragraf{Ocena za Dział} +\begin{longenum} + \item Ocena za dział ustalana jest na podstawie średniej arytmetycznej ocen z wszystkich zadań w ramach tego działu. +\end{longenum} + +\paragraf{Ocena za Poziom} +\begin{longenum} + \item Ocena za poziom ustalana jest na podstawie średniej arytmetycznej ocen z wszystkich działów w ramach tego poziomu. +\end{longenum} + +% ------------------------------- +%-------------------------------- +% \paragraf{Punktowanie zadania} +% \begin{longenum} + +% \item Procentowy udział zdobytych punktów oblicza się według wzoru: +% \begin{equation} +% \% = \frac{\sum_{i=1}^{n} p_i}{\sum_{i=1}^{n} P_i} \times 100\% +% \label{wzor:procent} +% \end{equation} +% gdzie: +% \begin{longenum} +% \item \(p_i\) – liczba punktów zdobytych za realizację \(i\)-tego wymagania, +% \item \(P_i\) – maksymalna liczba punktów przypisana do \(i\)-tego wymagania. +% \end{longenum} + +% \item Ocena końcowa zadania, zwana dalej „oceną”, ustalana jest według następujących progów: +% \begin{longenum} +% \item \textbf{Ocena 6 (celująca)} – przyznawana w przypadku uzyskania co najmniej 95\% maksymalnej liczby punktów, +% \item \textbf{Ocena 5 (bardzo dobra)} – przyznawana w przypadku uzyskania co najmniej 80\% maksymalnej liczby punktów, +% \item \textbf{Ocena 4 (dobra)} – przyznawana w przypadku uzyskania co najmniej 65\% maksymalnej liczby punktów, +% \item \textbf{Ocena 3 (dostateczna)} – przyznawana w przypadku uzyskania co najmniej 50\% maksymalnej liczby punktów, +% \item \textbf{Ocena 2 (dopuszczająca)} – przyznawana w przypadku uzyskania co najmniej 30\% maksymalnej liczby punktów, +% \item \textbf{Ocena 1 (niedostateczna)} – przyznawana w przypadku uzyskania wyniku niższego niż 30\% maksymalnej liczby punktów. +% \end{longenum} + +% \item Ustalenie oceny, zwanej dalej „daną oceną”, następuje w sytuacji, gdy osiągnięty zostanie minimalny próg realizacji zarówno \textbf{Wymagań Ogólnych}, jak i \textbf{Wymagań Szczegółowych}, określony w niniejszym przepisie. W szczególności: +% \begin{longenum} +% \item Aby przyznać ocenę \textbf{3 (dostateczną)}, wymagane jest zrealizowanie co najmniej 50\% wymagań przypisanych do zadania. +% \item W odniesieniu do pozostałych ocen, minimalny procent realizacji wymagań musi być równy lub przekraczać progi określone w odpowiednich punktach. +% \end{longenum} + +% \item W przypadku stosowania dodatkowych progów lub wymogów, takich jak system „50 na 50”, warunki te muszą być wyraźnie określone w opisie kryteriów oceny zadania, a uczniowie powinni zostać o nich uprzednio poinformowani przed przystąpieniem do wykonania zadania. +% \end{longenum} + %------------------------------------ %------------------------------------